I ran across this interesting paper by Frieder Kropfhäußer and Marco Sunder. They study the relationship between body mass index (BMI) and life satisfaction for about 8,000 Germans measured from 2003 to 2011.
Life satisfaction was measured via survey by asking people how satisfied they were with their life on a scale of 0=dissatisfied to 10=satisfied.
I used their estimates for all men and all women in their table 3 to construct the following graph.
They find no statistically significant relationship between BMI and life satisfaction for men (after controlling for earnings, age, education, and marital status). If you had to predict the BMI that would yield highest life satisfaction for men, it would be 36 - well into the obese range.
For women, there is a clearer relationship. Even still, the life-satisfaction-maximizing BMI for women is about 29, at the upper end of overweight and almost obese.
Now, maybe BMI affects earnings or marital status, which then has an indirect effect on life satisfaction; however, these results suggest that overweightedness in and of itself doesn't have much effect on the stated life satisfaction of men, and the "optimal" for women is far above what obesity researchers consider "normal."
It's hard to reconcile these findings with so much of what we read about obesity.