My players recruited a npc that I didn't 100% plan for. I'm using the Spellcaster Healer stat block for it, but I'm replacing a couple of the Cleric spells with Druid ones of the same level. The party is 4th level players, (a paladin and a warlock) and now the 4th level sidekick. My first impulse was to just start balancing as if I now had 3 4th level players, but the Sidekicks seem a whole lot weaker than players so I'm assuming that might make things harder than I really want them to be at this point. So how should I do it?

Treat it as three 4th level players, but give yourself some flexibility to scale the encounters on the fly. As long as you are comfortable adding environmental hazards and extra mobs as needed, you shouldn't have any issue challenging your players without killing them outright.

For a more dynamic game, consider the enemy's motivations. Creatures can think tactically and have self-preservation instincts, which can make encounters turn suddenly. A dragon might be able to defeat the party, but it values its own life over whatever paltry trinkets they may have. If they can get it to half health, it will probably just flee, rather than fight to the death.

The xp (if you use it) awarded after should be as if the party were three 4th level characters.  As such, the encounter should be balanced based on three 4th level characters.  A sidekick is comparable in power to a (non-optimized) PC, they just have less options. 

Also, keep in mind that the game is designed around a large number of relatively weak encounters.  If you deviate from that, (most of us do) encounter balancing becomes trickier, and with characters more likely to actually die if you mess up.

I would probably treat it as its level -1 for most purposes. That is, if you have a level 4 party, I would treat a 4th level sidekick as if it is 3rd level. It wouldn't actually be level 3, mind -- I'd just treat it as such, because statistically and mechanically, a 4th level SK cannot do all the things a full PC of that level could do. They don't get anywhere near the # of special abilities as they level up that a PC in a real PC class would get, for instance. Additionally, they are not run by another player so they do not represent another "player brain" to help the party figure out tactics, trap avoidance, puzzle solving, etc. If you run the SK, then as a DM you have to be very careful not to feed them too much info, solve the problem for them, etc. Even if you do, then YOU are solving it, not them, so they don't deserve full XP for it. A way to mediate against that is by treating the SK as a slightly lower level which would award the PCs marginally more XP per encounter, etc. And it would codify the reality of the game play which is that either as a DM running the NPC you are going to do the average, not optimal, thing tactically (I assume), or that the players are running the NPC and don't have another player who runs that character to consult with, have ideas, etc.

Have a similar situation in one of mine I am counting the NPC as half a player and trying to keep them about a level below the player characters, many because I don't want her over shaddowing any of the player characters, balancing combat she is almost a character but the players have to decide what she does and she isn't as much help in dealing with other situations, so I don't really need to account for her then.

I don't think you need to keep the SK below the player level... I just recommend counting it 1 level lower when calculating CR for encounters or things like that.

SKs shouldn't overshadow PCs... they have way less abilities than a typical PC has of the same level.