Rule 1 - talk to your players.

I suspect that a little less focus on their backstories won't offend them.

Smaller groups may find fights much more challenging, as there may be a needed role not being filled.  Not only does it risk upsetting a friend, it might make your job harder instead of easier.

Backstories are meant to be a convenience to the players in that it helps them zero in on their goals and motivations, and an aid to the DM in that it may provide future subplot hooks or useful NPC's.  By no means should it make your job harder, and if they players are expecting you to cater your game to their backstories so much you are getting tired of running your game, then drop your efforts entirely to work them in entirely, or maybe focus on just one subplot from one of the players at a time while you drive the main plot of your campaign on.

The over-arching rule of games is the Rule Of Fun.  Included in that rule is that *everyone* at the table must be having fun, and that includes the DM.  Talk with your players, tell them how you feel, and see what you can work out.

I don't think you'll find much difference between 3 players or 4, considering 3-4 is meant to be the ideal party size.

I'd also agree with the above; backstories aren't necessarily a focus. They come up now and again, sure, if you think you can produce fun content for the group out of a seed in someone's backstory, but just as often you can feel free to just let backstory be a roleplay guide for how you expect a character to act/how the character is treated by the world. 

There's two competing philosophies about character backstories: the first is that you're probably already thinking; that this is the characters' story and everything should tie together nicely. The second is that the story is the story and the characters belong to it, not the other way around, and it should be the characters' actions that shape events, not their backstories. 

I wouldn't say either philosophy is ever 100% correct, but you definitely want to strike a balance between them. If character backstory is taking up too much of your prep time as a DM, then I would rather adjust the significance of backstory in the campaign than ask a player to leave. 

Quote from Farling >>

Rule 1 - talk to your players.

I suspect that a little less focus on their backstories won't offend them.

 This. As long as you make it clear that the point of backstory in this campaign is to provide motivation and context, *not* plot hooks, they’ll be okay with that. Doubly so if they’re your friends! They probably care a lot more about hanging out with you than having some sort of perfect story.

And if you’re feeling burnt out with this campaign, be honest with them about that. Finish it up a bit early and move on to the next one. Maybe ask some of your friends if they want to try some one-shots in the in-between.

Remember, backstories aren’t important.  It is just your background + maybe a brief blurb about how they got their start in a class.  Anything more is unwarranted. 

Backstories are a giant trap that newer DMs fall into feeling like they need to care.  This game is about plundering dungeons and slaying dragons, stay focused on that! ;) 

Are you trying to focus on ALL of the backstories at the same time? If so, just focus on one at a time (and you can even limit how much of that one goes into the campaign), and put the rest on the back burner for a while. 

How I approach a game day is:

Elements of the story that are important to all the group - This becomes the focus of the the session

Elements of the story that are important to one or only some of the group (usually where backstory elements will end up) - Depending on the session, I will thread 0, 1, or 2 elements specific to one PC or a sub-group. I will keep track of this and circulate through the PCs personal stories in future sessions so no one's personal elements get stale.

For me, this keeps the session relevant to all the group by focusing on the main story, while making sure that none of the players feel like their personal story elements are being ignored.

I'd second the comments of the other posters.

1) You won't find that much difference between 3 and 4 players. 4 and 7 on the other hand is a significant change :) ... however, a party of 4 character is more resilient and a bit less likely to TPK if the DM under estimates the threat level of an encounter.

2) Working character backstories into a plot line can be fun but it honestly isn't the point of the game. The characters don't live their lives looking backward hoping to resolve something that happened in childhood. The characters are usually motivated by the present, by their current goals and objectives and those of the other people they are adventuring with. If occasionally some of those goals and objectives link into a character backstory then that is cool but if you are finding that "fitting in 4 backstories is pretty hard for me" then I would say you are misplacing the focus of the story line. The storyline is about what is going on in the world and how the characters interact with it and, to be honest, usually, most of what is going on likely does not directly to connect to any of the characters - when the characters find a bit that does it becomes a gem in the plot line where they go "cool!".

3) You say that DMing is getting tedious and that having 3 players would give you more "freedom" - take a close look at those feelings and try to figure out exactly what is causing them. If you aren't enjoying the plot line - create one you DO enjoy whether it directly involves the characters or not - it is always possible to drop in vignettes that are relevant to individual characters at almost any point in a storyline. However, I am wondering if there is something more going on that is making DMing less than fun for you in this case. Either way, after you have given it some thought, if you want some changes then talk to the players and see how it goes. Communications is the only way to resolve issues like this.

I can't say anything that David42 didn't already say better. I will lend some perspective in that about 10-15% of my game is related to player backstories and I'd be surprised if all 4 of your players thought it really important that the adventures include their backstories in them.

Backstories are backstories for a reason. They explain how you got here, but they are not the real story. The campaign is the real story. Tying the two together is great for world continuity, but you can do this with small things like an NPC or reference to an event. Backstories don't need to be (and really shouldn't be IMO) the main focus of the party's adventures.

tl;dr you don't necessarily need a change in group size, but rather group dynamics in what players expect the DM to accommodate

Simply tell players their backgrounds are getting in the way of the game you want to play as DM.  It sounds like the backstories are blown out of proportion.  Show them what the PHB provides as guidance for a background: 2 personality traits, 1 ideal, 1 bond, 1 flaw, pick a "background".  That's it.  It's to be touched upon occasionally but not to be dwelled upon.  I've said this before, but backstories of the sorts that extensively interfere with the campaign so that the DM has to tailor the game to it ... those tend to come from players who think they're role playing at an advance level whereas in actuality, roles actually performed by professionals -- the background rarely comes to the surface of the performance.  The background can help show how a characters' personality may respond to an event, but it shouldn't be the event.

If players insist on backgrounds, limit them -stirctly- to say 75 words per level.  Ideally that word count will become occupied by things the character actually does in game, but if they want to retrospect, that's probably ok at that work economy. 

So level with them saying you don't think your role of DM is to respond to background, but rather give the characters an environment to go forward in.  Then speak about how entertaining the backstories has made DMing unattractive so the possible changes are, someone else DMs (or they find a new DM), you reduce the table and let them figure out who goes, or they play in a way that's amenable to your DM style.  

Background is for the player to keep in mind, not the DM.

If they want to write stories about their characters, they can, but that's called fiction writing.  If they want you to DM, they need to give up some of that authorship and allow the game to happen.

Backstories are the the paper cup your cupcake comes in.

They are important only so far as to get the good stuff to your mouth.

Meaning if you ignore it, it's not a big deal because the cupcake and frosting are what matters. 

Quote from Wysperra >>

Backstories are the the paper cup your cupcake comes in.

They are important only so far as to get the good stuff to your mouth.

Meaning if you ignore it, it's not a big deal because the cupcake and frosting are what matters. 

I like that. Of course, I'd also argue that it's best to throw out your paper wrapper while consuming your cupcake, so read the implications of that on the analogy as you will.  I mean I think the paper is integral to the actual baking of the cupcake, but shouldn't really be consumed as part of enjoying the cupcake.

A lot of interesting perspectives.

Backstories can be really cool.  What do your players want though? Ask them first.  If they want their backstories to help shape the narrative then they want it to matter. If they are like, don't care, then why spend time on it?

Also to reduce the amount of time I am brainstorming and scheming about this stuff, I delegate some activities to players from time to time. When it comes to backstories I try to work the story with them to a degree so they are even more invested in how that plays out. rather than some expectation that the DM does all the work, get the players more engaged in doing some of their own work. If they really care about backstory engagement they will gladly assist. If they don't then they probably don't actually care about the backstory being woven into the campaign anyways.

I have had a lot of success using backstories to help strengthen the bond players have to their characters and increase their roleplay ability (of course bonds, ideals, flaws, etc help a lot more with that) but backstories can have some really cool narrative threads to pull on and create plot hooks and points to bring characters and players together more or find catharsis in that player's hero's journey.

Once again depends on what the players want. If they just want to hack stuff and find loot, that is great too, and in this case what is a backstory haha?

I was getting a little burned out on my campaign, and going to once every two weeks really helped. Kicking 1 guy out of 4 seems really harsh. Even kicking 2 would be better. Misery has company then at least. If you had 6 you could recruit one as a DM and split into two groups of a DM and 2 players. I'd try to avoid kicking anyone out.

The answer of course is always talk to your players. One might already be thinking of quitting or joining another group and take the opportunity. Maybe one of your players doesn't care much about backstory and won't miss weaving his backstory into the game.

In the big campaign our group is going through, 2 of the 4 of us have backstories that warrant some kind of follow up/progress.  The other 2 (one being my character) have a backstory that kind of sets them up to BE here and little else, meaning we (our backstory) can be ignored for the most part.  The other 2 have tales that would drag our group in vastly different directions, if we were to try and follow each.  Thus our DM offered breadcrumb trails leading off.  We are heading towards one, with the understanding that we MAY pick up on the other afterwards.  No promises though, lol.

Focus on the campaign, and maybe keep brief notes of things from the backstories that could be slid in to the tale for flavour.  Don't fret too much on not fully fleshing out some obscure tidbit from everyone's tale.  Also, as my signature states and several others have stated, talk to the players about it.  I would bet you have 1 or more who would prefer to see the campaign progress and their personal backstory simply fade away if that is what works best.

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Quote from pavilionaire >>

I was getting a little burned out on my campaign, and going to once every two weeks really helped. Kicking 1 guy out of 4 seems really harsh. Even kicking 2 would be better. Misery has company then at least. If you had 6 you could recruit one as a DM and split into two groups of a DM and 2 players. I'd try to avoid kicking anyone out.

The answer of course is always talk to your players. One might already be thinking of quitting or joining another group and take the opportunity. Maybe one of your players doesn't care much about backstory and won't miss weaving his backstory into the game.

 I am already going every two or three weeks but it still happens to me because there is not only DnD to me, even though I would wish that I could be able to spend all my time with it :/