In the aptly-titled working paper Does Health Insurance Make You Fat?, Stanford's Jay Bhattacharya and three co-authors looked at results of an experiment where Americans were randomly given different levels of health insurance (or no health insurance at all). They found that people with health insurance tended to gain weight. Private insurance policies increase the average person's body mass index by 1.3 points, while public insurance increases it by 2.1 points.
To put that in perspective, a 2.1-point increase for a six-foot male who weighs 150 pounds would be a gain of 15 pounds. That's a pretty powerful insurance policy.
This is a great example of the moral hazard problem. Being obese tends to cost more than being healthy (US$732 per year, according to a reference in the study). But if we have health insurance, suddenly it's more desirable than it was previously to be overweight. So people can exercise less and eat more as a result.
"[B]y insulating people from the cost of obesity-related medical care expenditures, insurance coverage creates moral hazard in behaviors related to body weight," the authors note. It's something to think about with the health care debate going on in the U.S. right now.