(When I lightly researched a while ago one of the topics the article you cited considers (correlation of health with weight in normal to overweight interval), I found that there is no consensus and there are studies giving contradictory conclusions. For causation, it’s even less clear, and the current position seems to be that weight doesn’t have a known causal role if around normal/overweight, instead exercise and diet affect both weight and health.)
(When I lightly researched a while ago one of the topics the article you cited considers (correlation of health with weight in normal to overweight interval), I found that there is no consensus and there are studies giving contradictory conclusions. For causation, it’s even less clear, and the current position seems to be that weight doesn’t have a known causal role if around normal/overweight, instead exercise and diet affect both weight and health.)