There has been quite some controversy over studies showing a positive impact on weight on longevity.
Katherine M. Flegal, PhD; Brian K. Kit, MD; Heather Orpana, PhD; Barry I. Graubard, PhD, "Association of All-Cause Mortality With Overweight and Obesity Using Standard Body Mass Index Categories - A Systematic Review and Meta-analysis" JAMA. 2013;309(1):71-82 write in the abstract:
Importance: Estimates of the relative mortality risks associated with normal weight, overweight, and obesity may help to inform decision making in the clinical setting.
Conclusions and Relevance Relative to normal weight, both obesity (all grades) and grades 2 and 3 obesity were associated with significantly higher all-cause mortality. Grade 1 obesity overall was not associated with higher mortality, and overweight was associated with significantly lower all-cause mortality.
An editorial in Nature, "Shades of Grey" writes:
"Walter Willett, chair of the nutrition department at the Harvard School of Public Health in Boston, Massachusetts, told US National Public Radio that “this study is really a pile of rubbish, and no one should waste their time reading it”."
"Critics of Flegal and of others who have reported similar findings take issue not just with the data used to make the claims, but the damage they feel that the claims will inflict on public-health efforts. [..] To discuss publicly results that threaten to undermine the simple message that ‘fat is bad’ will confuse doctors and the public, the critics say."
"The political mantra on public-health advice is clear: don’t send mixed messages. The media and those who get their information from the media prefer things in black and white: red wine is good for you; chocolate is bad for you. But, of course, science does not deal in black and white, hence the common criticism that scientists cannot make up their minds. One week, one group argues that extreme exercise is positive for health; the next week, a different set of researchers says the opposite."
I like the last paragraph...
"It is easy to see why those who spend their lives trying to promote the health of others gnash their teeth when they see complex findings whittled down to a sharp point and used to puncture their message. It is more difficult, from a scientific perspective, to agree that these findings should not be published and discussed openly, warts and all, purely because they blend uncertainty into a simple mantra. Make things as simple as possible, Einstein said, but no simpler. And simple, black-and-white messages can cause confusion of their own. All things in moderation — and that should include the language we use."
For more of the history on obesity studies see the Nature editorial: The big Fat Truth