That isn't true:

On average, healthy people lived 84 years. Smokers lived about 77 years and obese people lived about 80 years. Smokers and obese people tended to have more heart disease than the healthy people.

Cancer incidence, except for lung cancer, was the same in all three groups. Obese people had the most diabetes, and healthy people had the most strokes. Ultimately, the thin and healthy group cost the most, about $417,000, from age 20 on.

The cost of care for obese people was $371,000, and for smokers, about $326,000.

http://www.nytimes.com/2008/02/05/health/05iht-obese.1.97488... (numbers from 2008)