The meaning is that whomever uses this term is the worst kind of person. She is fat and usually disgustingly so(not thick, not pleasingly plump, not big-boned, sure as fuck not "curvy", or any other empowering word to put a positive spin on her obesity). However she is delusional enough to think she has any physically attractive qualities.
Note: Obesity doesn't make them the worse kind of person, its thinking they are beautiful/empowered or better than average while being fat. Similar to a borderline retarded valley girl who thinks she is anywhere near or above an IQ of 100
Some say that it refers to fat women whose face is still attractive, however any face bloated with krispy kreme donuts and fried chicken cannot ever be attractive ... especially when the disgusting stretch-marked tits and cottage cheese arms/thighs distract from the face.
Guy B: "I hate that, not only is she fat, but thinks it is somehow okay or even attractive. If there were any justice it would be legal to punch anyone who refers to themselves as BBW"
Guy A: "I know, the same goes for those creepy little guys with no self-respect who empower these whales by sleeping with them. Some guys will stick their dick into anything!"
Guy B: "Mark me down for electrical outlet or meat grinder before a chick who refers to herself as a BBW!"