You know dude, as someone who struggled with eating disorders of her own alongside massive self-esteem issues for YEARS, there is 100% a way to reach and maintain a healthy weight without counting calories or massively dieting. Similarly, a person can change her diet solely for her health, not necessarily for aesthetic reasons. What if you asked her to approach losing weight as taking care of herself as opposed to doing so to lose weight and change her appearance? If she changed her focus from "I am losing weight to look good" to "I am losing weight because I value my self and my health" she might be able to approach taking care of herself in a more positive way.

Does she exercise? The key for me was finding exercise that lit up my soul, not exercise I did purely to burn calories. I turned to yoga, cycling, walking, hiking, dancing, rock climbing, soccer, and my ultimate love: hoop dance. I love being active but love doing so in fun, playful settings, NOT the gym. This made all the difference. Maybe walk together or take a hike or bike ride together. Something that gets you both outside and together, doing something fun.

In all honesty, this issue goes far beyond you. She needs professional help. Your help and attention helps, but it will in no way solve her problems. A therapist, if she doesn't have one, is necessary. Can you help her find one? Living within an ED sucks the life out of life. She deserves to live fully and happily. But she needs to want to make change, any change, first.

Also no, you are not wrong in not being attracted to her. You sound like a really lovely boyfriend who is trying his best. We are attracted to who and what we are attracted to. If she won't try for change, it's not fair to either of you to continue a relationship.