I'm kinda in a similar situation. See, I met a guy online about 8 months ago and at first we were friends because he and I were both dating people. I started to fall for his personality. In fact, I started to like him more than my boyfriend.
He eventually broke up with his boyfriend and on August 8th, I did with mine. I asked him out the same night. He accepted and confessed to me that he liked me the whole time but was too shy to tell me.
I love him a lot but sometimes I find his appearance to be a bit unkempt. His long hair is the main thing I don't like about him. He is very fit and in shape and has an adorable face but his hair is just....not good.
I know it sounds super shallow but I cant help it. He always asks what I want him to change about himself and I always say "shorter hair" which he has done but then it grows back and he keeps it that way.
Unfortunately I have cheated, well not really. I mean I didn't sleep with anyone but I just kinda flirted with other guys who are slightly cuter. I felt really guilty about it so I stopped and told him what I did.
He initially got really upset and almost dumped me over it but later forgave me. I don't flirt around anymore though. I'm trying not to let something as superficial as hair bother me.
But as for your situation, it seems a little more extreme than mine. Your issue can definitely affect your relationship in the future if you let this bother you for too long. Body image is VERY sensitive to girls and many girls end up with an eating disorder if they feel like someone is making negative comments about their weight.
It's especially painful when it comes from a significant other. Someone that they love and trust. My suggestion is not telling her about her weight but instead, working out with her and maybe join a gym together. Encourage her that you want to help her be healthy, not because you are unhappy with her looks.
She will feel more confident if you do it with her rather than having her go by herself. Both of you will feel MUCH better this way!! Good luck