A recent NBER paper finds (the quote is from a summary of the paper hence the use of the third person):

As the number of restaurants per capita increases so does BMI. The average BMI will rise by 0.09 percent if the per capita number of restaurants increases by one percent. The authors note that the rapid increase in obesity in the 1980s is partly an "unintended consequence of the campaign to reduce smoking." On balance, however, they conclude that "the increase in the per capita number of restaurants makes the largest contribution to the BMI outcome, accounting for 54 percent of the growth" in a pooled sample of men and women.

The findings may well be correct, but it seems to me that the reverse could be true--that restaurants tend to locate near fat people. More precisely, fat people might eat out more often and restaurants probably make location decisions based on the propensity of people in an area to eat out.

I'm also a bit suspicious of the results because "The authors can account for 79 percent of the change in BMI for males and one percent of the change in BMI for females."