I know this (probably) is a hypothetical question, so I expect some hypothetical answers. Which is good, as long as they are sound.
Would a real hunter gatherer gain significant weight if there is a long period (let's say 10 years) of real food abundance (more food than he can eat and relatively easy to find/catch)?
Of course he eats only the foods that he can hunt and/or gather.
Would his instinct and satiety-hormones protect him? Or would he become a lazy overeater and get obese?
(things that probably are related are: set-points and neolithic agents)