I'm looking for a short story that might date back to the fifties or sixties. Aliens make contact with Earth and, in a twist on that old sci-fi trope, they want women. But just the fat ones. Different standards of beauty and all that. The women are cool with it because they're basically treated like royalty.
The Wrong World By J. T. McIntosh, which appeared in Galaxy Magazine in December 1960.
The plot, as I recall it, is that human-like aliens conquered earth with nearly no significant resistance due to their overwhelming technology, including energy shields functionally similar to those in Dune.
Afterward, many of the invader's officers decide to stay on Earth, finding many Earthling women to be very beautiful. Many of the officers have human women as aides to facilitate integration. Strangely, the aliens find no trace of women depicted in modern art and media; it had all been destroyed during the invasion.
It's eventually revealed that the women the aliens find beautiful turn out to be those that human men find less attractive. Effectively, the humans have won by way of absorbing the near-human aliens into their own society by pairing them off with women human men don't want.
“They must have found out very early,” Breeli said, “that we were attracted to the Rubens type. And they thought something might be made of the fact. So they carefully prevented us from finding out the kind of girls they were attracted to. They needn’t have bothered. We must have seen some of the girls they think are beautiful, and didn’t give them a second glance.”
“You did,” said Margo.
“Who, for instance?”
“You’re not going to tell me she’s the Terran idea of a glamor girl!”
“Six years ago,” said Margo, “she was Miss America—just before she married Jack Green.”
The story can be read at the Internet Archive.