Not that I know of, other than like, GTA San Andreas. Skate also let you tip the slider up pretty far on the heavy side, I think. I can't think of any game where the main character was supposed to be heavy though. I mean, it was REALLY hard to stay fat in San Andreas. You had to work at it, cause there was a lot of activity to make up for with food.
Truth be told, I don't think a serious game where you had to be fat would market itself very well, and that's pretty much it. I mean, who wants to play an unfit character when it's so easy to be unfit in real life? It's an inhibitive condition and video games tend to be all about doing what you can't do in real life. I mean, making obesity out like it's nothing in a video game could be fun, but it doesn't really reflect reality, and it wouldn't fit well in a serious game.
I mean, it's the same thing for being really weak. Not many games have you playing really weak characters either.