1. Single men earn less money the heavier they are, while single women earn more money the heavier they are. (This is after controlling for several factors, including education, age, and whether they're raising young children.)
This might seem to counter the "perception that obese women are discriminated against in the job market far more than obese men." But as economist Marina Adshade notes in her blog post, these facts might be due to the fact that heaviness is a more severe liability for women than for men in the dating market. Thus, heavy women have a stronger incentive to earn lots of money for themselves.
Clearly, being on the higher-income side of a pay "gap" doesn't necessarily show that you have an unfair advantage over the people on the lower-income side.
2. Lesbians earn more money than straight women. The gap is about 40% before controlling for any of the factors that might contribute to the gap. And there are many such factors:
[L]esbian women are better-educated on average, are more likely to be white, live predominantly in cities, have fewer children, and are significantly more likely to be a professional. But even when you control for these differences, the wage premium is still on the order of 6%.Here's a very important insight from that second link, a post on a blog called Offsetting Behavior by economist Eric Crampton (I've changed Crampton's brackets to parentheses to be clear that I'm still quoting him):
[I]f correcting for the observables reduces the wage gap between lesbians and heterosexual women from around 40% (the paper cites average hourly wages of $18.70 for lesbians and $13.34 for cohabiting non-lesbian females) to around 5%, odds are pretty high that there are a bunch of unobservables also correlated with job performance that aren't captured in the wage regression.
More broadly: if you think it's implausible that employers love lesbians so much that they pay them extra for no good reason, then shouldn't you expect the same when looking at the male-female pay gap?