A lot, says Sarah Kliff (reviewing this Lancet study):

The Lancet researchers gamed out what would happen if the average weight in the United States decreased by about 1 percent, which works out to an average weight loss of 2.2 pounds per person. We would avoid up to 2.4 million cases of diabetes. We would see up to 1.7 fewer cases of cardiovascular disease. As a population, we’d add 16 million more “quality life years,” a scientific measurement of both lifespan and quality of life. How do we get there?

20 calories a day less, apparently. On the other hand, Kevin Outterson reads the same Lancet research and concludes that "very significant reductions in US caloric intake will save 0.6% of health care costs by 2020."