But the facts are more definitive—and dispiriting—when you look at who, exactly, is paying attention to the nutrition facts.

Consistently, it's women, more educated people, and wealthier people who are more likely to care about calories. That is, it's the very same people who are likeliest to already be a healthy weight in the first place.

In 2013, Gallup found that 43 percent of people pay a "great deal" or a "fair amount" of attention to calorie labels at restaurants. (Considerably more, 68 percent, pay at least a fair amount of attention to labels on food packages.) But they also found that women, college graduates, and people making $75,000 or more are far more likely to pay attention to either kind of nutrition label:

Attention to Calorie Labels, by Subgroup

Gallup also found that those who pay attention to nutrition labels were more likely to say they ate a "very healthy" diet, and less likely to say they were overweight, than those who don't. In 2010, Columbia University researchers similarly found that women with some college education were more likely to use nutrition labels, and the people who used the labels ate healthier than those who didn't.

Nationally, men are slightly likelier to be overweight or obese than women are. And as I've written before, because overweight women are harshly stigmatized and economically penalized, rich women tend to use their resources to stay slim. Therefore, poorer women (but not poorer men) are more likely to be obese than their richer counterparts.

CDC/The Atlantic

And in every demographic other than black men, college graduates are less likely to be obese than their less-educated peers.

The takeaway seems to be that calorie labels work, but only if people look at them and know what they mean. Even in a 2014 study that found that it was overweight women who were likeliest to read nutrition labels, those same women were also more likely to diet, exercise, and drink less soda. They were reading menu labels, in other words, because they were already actively trying to lose weight.

A lack of nutrition labels isn't the reason so many Americans are overweight; they're how weight-conscious people stay thin. As George Loewenstein, an economist at Carnegie Mellon University, put it to the New York Times recently, “The people who most need the information don’t know how to use it."

This isn't to say we should give up on menu labels, or that the new FDA rules are destined for failure. As Corby Kummer noted in 2009, one positive externality of stricter labeling requirements is that they pressure chain restaurants to offer healthier menu items. (Starbucks, for example, shifted from whole milk to 2 percent.) Those types of changes can benefit all consumers, even those who ignore calorie counts.

If anything, it's a call for better nutrition education in schools, as well as for policies that can help poor Americans catch up to their rich peers' wholesome lifestyles. Maybe if fresh produce were as cheap and convenient as fries and nuggets, for example, or if poor Americans had more money to spend on food, we could all eat healthier without doing a bunch of caloric algebra every time we have lunch.