Thanks very much for the link-- that's a story of ill-thought-out optimization that will probably come in handy as an example as well as for the specifics.

However, it's possible to be fat and healthy. Note that the mice aren't just eating ad libitum, they're also sedentary, and I'd be willing to bet that their food has the minimal nutrients needed to let them get by-- not comparable to the food they'd eat in the wild. It may also be relevant that they're not in the sort of sensory environment they evolved in.