The answer to this is usually a firm no unless you have money. Money is the great mask for all physical and personality problems. There are no relationships with hot, sexy stripper types in your future, no cougars will want to relive their youth with you, nobody will feel good to be seen with you unless…
You are "funny"
Not just mildly witty, not just having an average sense of humor, but full on, attention-whore, class-clown, Chris Farley humor. That gives them something to talk about with their family and girlfriends, an excuse for being with you. You amuse her, and you make her look good, it's win-win for her. It will, however, be a temporary, short-term fling unless you come into some money.
You are completely pathetic
This means that you have no self-esteem, and look like you will spend the rest of your life in lonely virginity unless someone takes pity on you. Then you get to be her charity case and the world will praise her for being a kind of Mother Theresa. Again, this gives her a ready-made excuse for being around you.
You are working on getting skinny
There is light at the end of the tunnel, and she can claim to have loved you when you were unattractive, and can tell herself that she is therefore unshallow. Again, you make her look good, and she will be able to boast about you and show you off when you finally get fit. She gets to motivate you, too, fix you up as it were, giving her a sense of power.
Note: All this might be different for fat lesbians.