The !Kung people were a hunter-gatherer tribe in South Africa that persisted with the traditional way of life into the modern era. They had tons of food (the mongongo nut is available year-round in "truly massive quantities") and were still fit by modern standards (even thin), so it's not merely a question of the availability of food. This lends credence to the idea that it isn't merely the quantity of food availability, but its unnatural palatability that makes people overeat.

http://ajcn.nutrition.org/content/71/3/665.full?ijkey=f7644b...