Alright, so the basic formula for push, drag, and lift weight is Strength Score X 30(2 per size larger than medium). 

Crunching the numbers and your lvl 20 Human Fighter with Strength 20 lifts about 600 lbs. That's way more than I'll ever lift, but nonetheless I found this oddly smaller than what I had anticipated.

So next we look at the epitome of Strength in a D&D character: the Barbarian. Taking it a step further, I decided to craft a Goliath Barbarian (because Grog is my favorite CR1 character). Goliath's count as large for the purposes of calculating Push, Drag, and Lift weights. At lvl 20, the Barbarian's capstone feature gets them a strength score of up to 24. So 24 X 30 X 2 puts Grog Jr's lift weight at 1,440 lbs. This is more like it I thought. More than a 1000 lbs is crazy strong. Little did I know I was in for even greater disappointment.

I decided to look up the Guinness world record for most weight ever lifted by a human. That's when I found Gregg Ernst. This absolute mad lad lifted WELL OVER FIVE THOUSAND POUNDS. Not only is that insane, but this dude lifted SUBSTANTIALLY more than a God-Tier Barbarian who descended from literal Giants. 

Long story short, I crunched some more numbers (Storm Giant, and then Tarrasque) and Gregg Ernst wipes the floor with the Storm Giant, and is beaten only by the Tarrasque (and at that by only 2000 odd lbs). This 6'0" Canadian man lifted an amount of weight approaching that of a creature designed to level civilizations. 

Obviously this isn't that big of a deal because this mechanic is hardly (if ever) used. I still think, however, that is is beyond ridiculous that my supposed dragon-slaying Orc Barbarian loses a weight lifting contest to some dude from Canada.

Quote from theBloodwolfe172 >>

I decided to look up the Guinness world record for most weight ever lifted by a human. That's when I found Gregg Ernst. This absolute mad lad lifted WELL OVER FIVE THOUSAND POUNDS. Not only is that insane, but this dude lifted SUBSTANTIALLY more than a God-Tier Barbarian who descended from literal Giants. 

 

Did he carry that weight for 8 hours or more and then fight some monsters while still carrying it?

So RAW, I agree with the rules for standard lifting, no extra rolls required.

In my games?  I agree with you for heroic lifting purposes.  Carrying capacity vs dead lift is a different story.  God tier dude from Canada lifted that for about 5 to 10 seconds before dropping it, and I’d let any character with the appropriate STR score attempt the same with an Athletics check, at a pretty high DC.  The Tarrasque lifts handles that much weight as a matter of fact, no exertion.  Canada man was doing it and rolling pretty damn well for the 10 second time frame and then dropped it like it was hot.  

How often do people even track encumbrance that closely?  My experience is that it's generally only something that gets attention paid to it in the video games.

It does feel a little low, but I’m with Spideycloned on this: those are the rules for lifting something you can definitely, easily lift even on a bad day. It’s a DC 0 Str check, basically. If you want to lift more, you can try. It’s just going to take an actual check to succeed.

The five thousand pound figure was a stunt type lift; his dead lift was 'only' 800 pounds. That said, a humanoid the size and shape of a storm giant (26' tall, fairly average build) would have a weight in the 15,000 lb range and should have similar lifting ability.

You can always steal the lifting rules from 3rd edition, in which case a Str 29 Storm Giant has a heavy load of 5,600 lb.

So I'm confused. Is your issue with the amount the guy lifted, or the fact that he's from Canada?

You compare much of any of the details with real life, you’re going to have the same problem.  It just wasn’t designed or intended to be directly comparable

There are really only two types of players who calculate this stuff.

There are theorists like the OP who want to find the max of a character to measure how epic they are, and there are simulationists who use these numbers throughout the game.

I think these rules fall in line with the desires of the simulationists - most I know would be fairly upset about a character walking around with 5000 lbs. of gear, even in epic. They are the ones that actually use these rules the most, so I think this makes sense. The rest of us are okay with just ignoring it or only applying it when a character is abusing your policy of ignoring it.

Quote from scatterbraind >>

I think these rules fall in line with the desires of the simulationists - most I know would be fairly upset about a character walking around with 5000 lbs. of gear, even in epic. They are the ones that actually use these rules the most, so I think this makes sense. The rest of us are okay with just ignoring it or only applying it when a character is abusing your policy of ignoring it.

The fact that max human strength is only twice average is a bit off, but the main situation where it causes issues is when you're looking at Huge creatures and above; an elephant only has 8.8x the carry of an average human.

one of the problems you're not going to get over is that D&D stats are linear..trying to line things up IRL wouldn't allow you to keep it that way and be so convoluted it'd defeat 5e's goal of simplifying things

Quote from HeathSmith >>

one of the problems you're not going to get over is that D&D stats are linear..trying to line things up IRL wouldn't allow you to keep it that way and be so convoluted it'd defeat 5e's goal of simplifying things

 Eh, it would just be a table with 29 values. Not a big problem. The actually hard part is that most people have no idea what anything significantly outside of human size weighs in the first place, so the lift numbers aren't usable in the first place.

Quote from Kotath >> 

Quote from scatterbraind >>

There are really only two types of players who calculate this stuff.

There are theorists like the OP who want to find the max of a character to measure how epic they are, and there are simulationists who use these numbers throughout the game.

I think these rules fall in line with the desires of the simulationists - most I know would be fairly upset about a character walking around with 5000 lbs. of gear, even in epic. They are the ones that actually use these rules the most, so I think this makes sense. The rest of us are okay with just ignoring it or only applying it when a character is abusing your policy of ignoring it.

 

If you look at the kinds of strength feats, Hercules, or Samson or Beowulf or any other mythological strong man could manage and then look at D&D, you realize that strength in 5e does not even compare well with RL let alone those fantasy examples. 

 What I'm saying is that the simulationists don't want the PCs to be Hercules. They want them to be pretty much just regular people like medieval knights or the survivors on The Walking Dead. 5e is an attempt to appease a very broad range of players and this is one of the places where they had to choose a group. They chose the one that is most likely to use the ruleset in the first place, as I'm sure their surveys turned up evidence that a lot of players find stuff like encumbrance tedious and unnecessary.

I'd probably delete weights from most things entirely and just have extrapolate Shove a bit. Probably something like

Shoving a Creature: make a Strength (Athletics) test against the target's Strength (Athletics) or Dexterity (Acrobatics) check. You have advantage if you are larger than the creature, disadvantage if smaller; this replaces any bonuses listed for specific powers that modify size. You automatically fail if the target is two steps larger.

Shoving an Object: you may also shove objects; instead of being resisted by a check, your target is the object's AC. Solid chunks of matter, such as boulders, should be counted as one step larger than their actual size.

Thus, if there's a Medium boulder blocking a passageway, you treat it as Large because it's a boulder type object, and then you have to make a DC 15 Strength (Athletics) check with disadvantage.

I can see where OP is coming from, but if you look at it as the lifting capacity being something "easily managable" and then from you apply an athletics check it makes a lot more sense to me... All those record breaking lifts would almost certainly be high dc athletic checks.. So if your goliath barbarian can lift 1400... I could allow them to lift a lot more provided they roll a decent check... If anything, real like extreme examples should give us an idea of how to set the DC of the check.

So if the worlds strongest man can lift something like 5k pounds under perfect conditions and form.. I'd let the goliath barbarian left something like that with a 25-30 dc 

Instead of going by weight, go by size.

Strength: size of burden carried without encumbrance
1 to 4: Tiny
5 to 8: Small
9 to 12: Medium (lightweight)
13 to 16: Medium (heavyweight)
17 to 20: Large
21 to 24: Huge
25 to 28: Gargantuan

I am not sure of 5e definitions, but "lift" used to indicate a full military press over one's head, not simply lifting off the ground.  

I'd just use the 3.5 Hieght to Body Weight chart, since it actually works really well as a weight lifting chart imo.
A Medium size creature can lift up to 500 without any ability to count as one size higher, sounds reasonable to me. A normal non-super muscular person could possibly lift that in an extreme circumstance if they needed to, likely with a roll involved. While a 20 str barabarian might not need to roll there depending on the situation (Like if your dm allows 'take a 10' in that instance).

Then you get into abilities like Powerful Build which I'd say is comparable to having the strength of a pro weight lifter. A large creature, which you would count as with powerful build, would then be able to lift upto 4000 pounds, which while falling short of the world record is much closer to it and much more believable.

And the chart actually keeps working well for this as they go up in size too. A 64 ft tall monster could lift upto a 2-3 story building minus the foundation/basment, depending on the items inside the building.
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The main problem would actually be a balance problem considering just how big a player can get. A low level Rune Knight can go large, a caster can cast enlarge on them to make them huge, and with powerful build they have the strength of a gargantuan aka the 64ft monster. And having a player be strong enough to throw a 2 story house would be a big balance issue. So maybe put a penalty on their lifting limit since they aren't naturally that size, or have houses protected in some way to prevent them from being picked up. Still let the player start smashing walls in but don't let em chuck it.
A high level Rune Knight can even reach the colossal lift range, like omg.
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So the chart works and in most cases doesn't cause issues, but for Rune Knights specifically you need to make a rule to prevent abuse.

Here's a link to a post on a different site that brings up the chart in question.

https://rpg.stackexchange.com/questions/195388/what-are-the-height-and-weight-size-ranges-for-each-size-category-of-creature#:~:text=Truncated%20below%3A%20%20%20%20Size%20Category%20,%205%20ft.%20%205%20more%20rows%20

I'd also like to point out that there's a huge difference between adventuring and power lifting. Power lifting is a job where they spend their whole day saccrificing their ability to do other things to lift ultra heavy stuff. (My cousin does it as a hobby, but she isn't going to contests)

Adventurers still need time and exercise to do more than literally lift. That much bulk would actually be a hinderance in a fight.

Heck, work out a deal with a wizard to wish for a new Manual of Gainful Exercise every week. You'll be lifting 6000# in a year easy.