Obesity is a modern epidemic, and we didn't all suddenly mutate. Environmental factors are much more impactful.

But not everyone got equally obese, even in the same environments, during these time periods. What portion of the population was predisposed to extra large impacts of unhealthy foods, sedentary lifestyles, external stressors, etc., when those environmental factors weren't as prevalent?

So for completeness, it's a bunch of feedback loops between genetic factors, epigenetic factors, and environmental factors, including cultural/social factors. Some genetic factors make it harder or easier in the environments we live in (and some environments make it harder or easier).