My girlfriend opened up about her abusive ex, and I don't know how to let her know how perfect she is...?

Okay, well I’m 17, and my girlfriend Melanie is 18 (and yes, we’re lesbians. If you don’t like that, please don’t answer.) Her and I were friends for about a year and a half, and we started dating about 2 months ago. However, because we were really close friends before we started going out, I know her really well, and I know that I’m crazy in love with this girl. She’s beautiful and adorable, and sweet and quirky and so kind and understanding. She’s the strongest person I know. In November, she’ll be cancer-free for five years, now, and I admire the strength she’s had even since she was a little girl to get through that. However, about a month ago, she opened up to me and told me some things about her ex girlfriend. I never liked her ex, as she was quite unfriendly, usually. Melanie told me that when they started dating, this girl (Jess) was very nice and everything, but almost right after the first time that her and Melanie got intimate at all, she started putting Melanie down.

She verbally abused her, and told her that she was fat all the time. Melanie is very small. She’s only 5’ and she’s VERY fit; she dances and works out and eats extremely healthy. She just happens to have very curvy hips and thighs on the larger side (not chubby, at all.) She told me that soon enough, Jess started hitting her and physically abusing her. She says she stayed with Jess because she had convinced Melanie that she was “annoying” and a “loser” and that no one else would “put up with her.” Luckily, she realized that the abuse was getting out of control, and got the strength to leave her. However, now I see the lasting effects that the relationship had on Melanie.

She always seems very confident around friends and all, but I’ve noticed that once her clothes come off, she gets extremely self-conscious. She hides her thighs and doesn’t like the attention to be on them or her hips. I tell her all the time that her curves and her thighs are ridiculously sexy to me (and it’s extremely true. I find her body so incredibly sexy), but she still hides them. Also, sometimes, she’ll cuddle up next to me on the couch, and I’ll shift or move my arm to put it around her, and she’ll flinch and move away from me a bit until I tell her “Mel, it’s fine, I was just moving my arm.” She’s just so fragile and self-conscious, even though she puts on an excellent act of confidence around everyone else. What can I do to help her realize how beautiful and amazing she is? I want her to know how perfect she is to me, but even when I tell her, she still hides her gorgeous curves and thighs. What should I do to help her overcome this? Any advice, please?