(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.)
An article about the pitfalls of using mice for animal research leads off with the example of calorie restriction. The controls for calorie restriction mice experiments were obese mice, suggesting that the health benefits of calorie restriction might be conflated with the health benefits of not being obese. I get the impression that people who study calorie restriction still think it worthwhile for life extension, but it's useful to try and integrate all evidence you come across.
[edit] timtyler suggests this is a well-understood effect that's already been taken into account by CR scientists.