There are two broad answers. The first is simply methodological. Understanding the causes and consequences of obesity is hard because scientists like randomized experiments—e.g.: give one group drug X, give another group a placebo, and observe the difference. But this is almost impossible to do with weight. It's unethical to randomly make participants obese just to watch what happens to them. So, it's useful to study compare data and try to find out how income and obesity are actually related. Essentially: To study weight like an economist.
The second answer is that obesity is an economic problem, plain and simple. Obese Americans costs the U.S. $190 billion in annual medical costs attributable to their weight—or 20 percent of national health-care spending, according to Cawley's research. That's a shockingly high figure, and it implies that unpacking the relationship between income and obesity could save America even more money and anxiety than many researchers estimate.
The trouble is that, when it comes to obesity, practically nothing is clear-cut, starting with the word, itself.
Obesity is broadly defined by a body-mass index—a.k.a.: BMI, a ratio of height to weight—over 30. But not all weight is the same. There are variations of fat and muscularity that can make perfectly healthy, muscular men and woman technically obese. If you switch measures to body-fat percentage, the black-white obesity gap among women falls by half. If you switch to skin-fold thickness, scientists can predict obesity decades before your BMI crosses the 30 threshold.
Equally murky is whether being poor leads to obesity. Cawley's own research didn't quite find causality (there is "little evidence that income affects weight," he writes).
Still, there is copious evidence around the world that obesity is a peculiar condition for poor people in rich countries. Less-developed countries have lower obesity, but in richer countries, there tends to be an inverse relationship between waistlines and bank accounts. It's what researchers have called the "health-wealth" effect: Wealthier people tend to be healthier people. In the U.S., rich white women and poor black men have the lowest obesity rates (followed by rich white guys). America's highest obesity rates by far are among poor minority women. A 2008 U.S. Department of Agriculture's review of the effect of food stamps found obesity didn't rise among children or men but did increase slightly among women.
So poverty might make some people obese, but obesity definitely makes many people poorer, through two broad channels: (a) it reduces take-home pay, particularly for women; and (b) it's related to health conditions that reduce discretionary income, too.
If there is there is a close relationship between weight and poverty, it is strongest among women, from the peak of the 1 percent to below the poverty line. At the top, corporate boards appear severely biased against larger women in a way they don't discriminate against larger men. Cawley's research found that obesity lowers wages for all workers but particularly for white women. Women who are two standard deviations from normal weight (64 pounds for the typical woman) earn 9 percent less, he writes. Obese women are half as likely to attend college, 20 percent less likely to get married, and seven times more likely to experience illness, depression, or death from being overweight.