In Greek mythology, the hydra was a monstrous multi-headed serpent with the ability to constantly regenerate: When one of its heads was cut off, two more would grow back in its place.

In the U.S., where more than one-third of adults are obese, public health has its own hydra-headed monster. Every risk factor identified for obesity carries others with it, all linked together in different ways: A person’s lifestyle habits like diet and exercise are part of the equation, but so is their environment. So is their genetic makeup. So is the stress they feel and the amount of sleep they get each night.

So is their income, but with yet another caveat: gender. For women, income is inversely correlated with obesity, according to the Centers for Disease Control and Prevention, meaning that fatter wallets correspond to thinner waistlines. For men, the opposite is true, though the connection is much weaker: Men at the top of the socioeconomic food chain are only slightly more likely to be obese than their less-wealthy counterparts.

To begin to understand why this particular difference of the sexes exists, it’s helpful to answer the question with another question: Which part of this equation is the cause and which is the symptom? Does being poor make women fat, or vice versa?

Most likely, it’s both.

A paper recently published in the Journal of Health and Social Behavior examines how these two factors work together and how they split along gender lines. Researchers tracked the long-term impact of obesity by looking at data from the Wisconsin Longitudinal Study, a large-scale project that collected health and social information from more than 10,000 people born in 1939 at multiple points in their lives. Consistent with the findings of the CDC, girls from poorer families tended to have higher body mass at age 18 than their richer female peers, a pattern that didn’t exist for boys. But the researchers also found that among the overweight teens of both sexes, the girls—and not the boys—tended to perform worse in school than their thinner classmates.

Later, at age 54, the subjects demonstrated two similar patterns. First, the women who had come from poorer families as children were more likely to be obese adults; second, women with higher body-mass index were more likely to be poor, regardless of their childhood status. As in adolescence, the effects were less pronounced and less consistent among the men of the study.

These discrepancies, explains study author Tetyana Pudrovska, may be rooted in our notions of what attractiveness looks like: For women, specifically, it looks thin.

“[Thinness] is more closely tied to physical attraction in our culture for women than for men,” she says. “Obesity violates cultural standards of female beauty.” As a result, the stigma of obesity is lopsided across gender lines, with women bearing the brunt of it.

The higher social price begins to take its economic toll as early as adolescence, she says, as the stigma of obesity can lower teen girls’ self-esteem—which, in turn, can lead to a host of problems that impede academic success. “Girls who are obese, they’re less likely to go to college and less likely to graduate from college,” Pudrova explains. “And one of the reasons is that they have higher levels of substance abuse in high school. They have higher levels of truancy.” Among the subjects of the Wisconsin Longitudinal Study, their grades also tended to be lower.

The same forces persist in the workplace as well. Already at an educational disadvantage, obese women face rough treatment at the hands of the labor market, where attractiveness is often rewarded: Women with higher body-mass index, earn less, on average, than their thinner counterparts, and have fewer opportunities for advancement. Wages for women tend to peak among those with a BMI of 21.8 (a healthy weight is considered to be a BMI between 18.5 and 24.9); for men, by contrast, the wage-weight connection punishes only those at the highest end of the BMI scale.

As Olga Khazan reported earlier this year, obesity is expensive. Obese men lose an average of $2,646 each year to things like additional insurance costs, sick leave, disability, and lost productivity. For women, that figure is $4,879. The difference? Lower wages.

But just as weight keeps women from advancing economically, a lack of economic opportunity keeps weight high.

First of all, poverty is marked by uncertainty. Shift work makes it hard to plan time to exercise; juggling multiple jobs makes it less likely that a person will have the time at all. And when time is a precious commodity, spending it on planning a diet or cooking a nutritious meal seems a lot less appealing (and diet pills seem all the more so).

Second of all, poverty is stressful. There are a number of reasons why stress might lead to weight gain, but Ezra Klein explained a big one in The Washington Post in 2009:

Obesity is bad, but it may just be one of many bad things. Overdue bills. A horrible part-time job. Endless communing time on the bus. A mother with diabetes.  A child running with the wrong crowd. A leaking roof. In that scenario, slowly reversing your weight gain might be a good idea, but it hardly makes a dent in the overall crumminess of the conditions. It won’t replace pain with pleasure. So you do things that are surer to replace pain with pleasure, like have a delicious, filling, satisfying, salty, fatty meal.

But this strategy isn’t implemented equally: As the American Psychological Association has reported, women, more than men, tend to use food as a means of coping with stress.

It’s one more variable in a tangled mess of variables that all point to the same conclusion.

“Body mass and socioeconomic status are simultaneously antecedents and consequences of each other,” the researchers wrote, “via mutually reinforcing patterns of effects.” Or, more simply: Obesity leads to poverty leads to obesity, bolstered all along the way by ideas of the acceptable female body—and consequences for those that don’t measure up.

“There’s this vicious cycle,” Pudrovska says. “This social disadvantage early in life launches this reciprocal chain, especially among women, so it’s not sufficient to address only individual behaviors to reduce obesity.”

In a column last year on the obesity-poverty link, The New York Times declared: “The articulated goal should not simply be to create a population of poor people who are thin, but to create a population of poor people who are less poor.” As the research shows, though, even that is just one part of a multi-headed issue; gender is another integral part of the same beast.