Lag With Higher Screen Size/Resolution

ShadowGypsy23​  The problem could be your graphics card, at least in the immediate sense.  I play at 2560x1440 and get some stutter, mostly related to animals (it's barely there when the Pets expansion is disabled), but I have a much faster GPU.  But the underlying issue is not necessarily that the card is underpowered overall.

Sims 3 can only use 800 MB of video memory; this limit can't be overcome by mods or standard tweaks of the game files.  This amount of VRAM may not be enough to cover all the data your game is generating at higher resolutions, although it's impossible to say for sure because the game tends to load all it can into VRAM no matter what the situation, i.e. monitoring VRAM use wouldn't give you an answer because the game would always be using the max 800 MB.

So the game has to swap a lot of data back and forth, and rather quickly, and possibly a lot more at higher resolutions (even on lower settings).  The rate at which your GPU can perform these swaps is going to be much lower than with higher-end hardware.  So it's not performance in the sense of the usual benchmarks, but it's still about the overall specs of the card.

However, all this is speculation.  There could be something about the world you're playing in or other changes you've made.  The Tiny UI Fix has its issues too, so I'd test without it.  And test a new save in Sunset Valley to make sure you're seeing the same thing.

As for a possible fix that doesn't involve spending money, you could look into DXVK for Sims 3.  There are a few tutorials out there, including this one:

https://nornities.tumblr.com/post/751283334185959424/how-to-use-dxvk-with-the-sims-3

The point is that among other things, the VRAM cap is raised or removed.  So if that's the issue, you should see a major difference.