A new NBER working paper says it does:
An increasing number of Americans are obese, with a body mass index of 30 or more. In fact, the latest estimates indicate that about 30% of Americans are currently obese, which is roughly a 100% increase from 25 years ago. It is well accepted that weight gain is caused by caloric imbalance, where more calories are consumed than expended. Nevertheless, it is not clear why the prevalence of obesity has increased so dramatically over the last 30 years.In New Zealand, there's a strong income gradient in obesity and in smoking prevalence. The government's been pushing hard on anti-tobacco measures. More poor people in absolute numbers will be quitting smoking than will rich folks, even if richer folks are more responsive to anti-smoking messages, just due to base rates. And so we expect the income gradient to get stronger (poorer people get fatter) as the government keeps ramping up restrictions on smokers. Net effects on health are probably still positive - smoking is still probably worse for you than obesity.* But whatever the estimated benefits of policy, they're overestimated if they don't account for the consequent rise in obesity.
We simultaneously estimate the effects of the various socio-economic factors on weight status, considering in our analysis many of the socio-economic factors that have been identified by other researchers as important influences on caloric imbalance: employment, physical activity at work, food prices, the prevalence of restaurants, cigarette smoking, cigarette prices and taxes, food stamp receipt, and urbanization. We use 1979- and 1997-cohort National Longitudinal Survey of Youth (NLSY) data, which allows us to compare the prevalence of obesity between cohorts surveyed roughly 25 years apart. Using the traditional Blinder-Oaxaca decomposition technique, we find that cigarette smoking has the largest effect: the decline in cigarette smoking explains about 2% of the increase in the weight measures. The other significant factors explain less.
For those reckoning that this just means we need to stomp on unhealthy foods while we stomp on smokers, do note that their results on obesity suggest that food prices have very little effect on obesity rates. They say that because the effects of food stamp programmes and of urbanization on obesity have been very small (for the worse), the effects of weighting food stamp programmes towards healthier options or of building more bike paths are similarly likely to be small. They note further, and specifically, that fat taxes are likely to be ineffective: they find no evidence that food prices (regional variation in foot-at-home or fast-food prices) or of restaurant prevalence have effects on weight.
* Which one generates larger negative technological externalities is difficult to determine a priori.