PhysicsGirl:
If she's 20 lbs from "hot" she's really not all that fat, if fat at all. Contrary to what the magazine racks and hollywood say, a woman who is a size 6 or size 8 isn't fat. You also assume that she has poor eating habits. A definite stretch.
FWIW, I weigh 15lbs more than I did when I started dating my husband. That was 10 years and one child ago. Have I let myself go? Not at all. I'm a size 6 and I used to be a size 2. So PhysicsGirl knows her physics, and depending on LW's height, 20 pounds might not be so far from "hot."
I don't think someone is shallow if they want their mate to lose weight. And physical attraction is important, which is why I usually listen when my husband asks me to wear certain clothes, or to keep my hair long, etc. Sure, it's my body and I get to say what goes on it or in it but because want to look attractive to him, I value his opinions. I don't think it's controlling to ask that your mate do things that make him or her more attractive to you.
BUT holding out on committing to a person unless she conforms her appearance to your exact specifications is controlling, in a creepy way. Run, LW, run!!