Fat of the Land

I wonder why only humankind suffers from obesity? Well of course there are the animals that people make fat against their normal behavior like cats, dogs, cows, sheep, ducks, salmon, (rice, soya, tomato) etc. If over eating is sickness why don't other animals suffer from it.

Already in ancient Rome they used to eat all day long and then put their fingers in their throats to make some more room for smoked big and wine grapes. But I guess fat people were around before that. Can someone tell me at what point of our short history fat people started walking amongst us?