Another problem with the debate is that when we hear (I know I've been guilty about this) "Obesity is not killing us", we go, "WTF ?" because we're thinking of the morbidly obese, who comprise all of 3% of the population and which do die earlier ... just like the underweight.*
But in the VERY broad middle we see tens of scores of millions of Americans that we fitness-minded types would consider fat, but who may well outlive us.
*Although even here I've seen research which has the most morbidly obese of women outliving normal weight males.