It took several millenia for artists and writers to finally put clothes on their ideal male characters and another before they started depicting male protagonists as less than ideal and quite a bit more time before there were female protagonists at all and even then, that was in Romance novels and mysteries. It's really pushing it to ask this question about games alone when it's tough enough to find them outside of games. People don't celebrate the commonplace,and in the process, miss out on an opportunity for genuine drama that only comes from use of characters not in the peak of human physical performance.
A fat man running from a jaguar would be a more tense scene as one would have no way to know where the writer is going with the scene (unless its a horror movie and he isn't the star, in which case, everyone knows what will happen next...kitty gets a full meal)whereas an Alpha-Male rugged He-Man type character would just wrestle the jaguar down then turn him into a house pet.
That said, one chapter of Eternal Darkness:Sanity's Requiem has an obese main character. If you consider The Godfather Don Vito Corleone to be the main character of the Godfather game(he's the titular character, at least),there goes another example.
I for one, would enjoy the challenge of playing someone with health problems or, at the very least, justified mobility problems in survival horror.
Well, you can make your own in The Sims 3, not that its particularly easy to play that as a drama(but, by Golly, I do try! One of my first acts as a Queen latifah-esque Lady Killer was to break up the happy LandGrabb home by stealing Nancy away from Geoffrey then beating him up on his own front lawn, doubling his humilation!).
