There is lots of evidence, of several different kinds.
At the biochemical level, we actually know a lot about some of the pathways that allow food and body fat composition to govern appetite. See, for example, leptin signaling.
At the anthropological level, we have good examples of several different pre-agricultural societies where food was abundant and obesity was rare.
At the whole-animal experimental level, researchers have demonstrated in both rats and humans that when you give an animal unlimited access to food, it doesn't gain unlimited weight. It reaches a plateau and then resists further changes up or down from there. Interestingly enough, rats fed a diet of unlimited human junk food reach a much higher plateau than rats fed a diet of unlimited standard rat chow.
And finally, we all know people (perhaps even our younger selves) who never consciously worry about what they're eating yet undergo very little fluctuation in weight. Judged from the perspective of a control system designer, getting that kind of stable outcome from wildly varying inputs doesn't just happen by luck. And indeed, experimenters have shown repeatedly that "naturally lean" people experience reduced appetite in the days following a period of overeating. You can even deliberately perturb the system by force-feeding them, and they bounce right back to their long-term weight thanks to reduced appetite and increased metabolism.