Obesity epidemic is a very recent phenomenon. Are you arguing that there were no societies that had caloric surplus up until late in the XX century?
Or would you say that American Samoa with obesity levels of 70% [1] somehow have the luxury of having calorie surplus, while people of Switzerland (8.2% obesity) are struggling to get enough food?
Speaking about Paleo diet in particular, why don't those guys gorge themselves into obesity [2]?
The Kitavan people have been under greater study for their remarkable health characteristics. The people show no indication of coronary heart disease, stroke, diabetes, dementia, congestive heart failure, acne, low or high blood pressure, or obesity. There is also almost no indication of cancer.
The Kitavans have abundant food supply and are not threatened by malnutrition or famine.
[1] https://www.cia.gov/library/publications/the-world-factbook/...