I think this study corroborates what you are saying
http://jama.jamanetwork.com/article.aspx?articleid=200731
Results Relative to the normal weight category (BMI 18.5 to <25), obesity (BMI ?30) was associated with 111 909 excess deaths (95% confidence interval [CI], 53 754-170 064) and underweight with 33 746 excess deaths (95% CI, 15 726-51 766). Overweight was not associated with excess mortality (?86 094 deaths; 95% CI, ?161 223 to ?10 966). The relative risks of mortality associated with obesity were lower in NHANES II and NHANES III than in NHANES I.