Jeff, if you want/like her, be different than most men and just talk to her. Talk to her as an adult, be polite, sensitive and direct. When she says she isnt doing well etc etc, tell her. Something like : of course you arent feeling alright. I understand why. It is all a misunderstanding and I would love to clear this out. I am in love with you. I am with you because I like/fancy/whatever you. YOu can choose to ignore this and hold on to your false assumptions or accept the fact I am on board and have fun together. And then let her sleep on that.
I am very self guilty about my looks/weight. My sexual life, my mood, my humor, all get affected when I dont like myself. I remember how great I felt when I was told "you gained weight? Good. More of you to love" and there was no discussion dwelling etc over it. It was stated as a fact to me. I was left alone to decide which reality I would focus on. I chose the "positive one". I felt I would be stupid not to. Hugs M