That's a comforting story from freakonomics. It's not true.

From the World Health Organisation web site:

'Being overweight or obese can have a serious impact on health. Carrying extra fat leads to serious health consequences such as cardiovascular disease (mainly heart disease and stroke), type 2 diabetes, musculoskeletal disorders like osteoarthritis, and some cancers (endometrial, breast and colon). These conditions cause premature death and substantial disability.'

Just look around, who dies first of people you know?

QJS