I can’t think of many where this is the central idea at the moment, but a couple games that touch on this below. I’ll add more if i think of them.
Love at First Bite is a short “catch-the-falling-object” game, objects in this case being food, with your character getting slower the more she eats (FWG)
The Nebutori’s Tale is a Quest text adventure game about trying to break a weight gain curse. Pacing is slow at the beginning (you need to grind the first 14 days minimum without completing the main quest before you start putting on big weight), but there are relevant descriptions at higher weights, and you eventually need a scooter to move around one location. (FWG)
The Curse of Something is a furry male slice-of-life/light-RPG. As you gain, if you don’t have enough corresponding muscle mass, you will lose max energy needed to do activities both in battle and in town (MWG)