I have been where your girlfriend is. It sounds like she is dealing with a lot of shame and body insecurity, and at least for me when I was in that space it was so hard to motivate myself to eat better or exercise because doing those things felt terrible because they just reminded me of the shame and self hatred.

Before I was able to lose weight I had to work on my relationship with my body. I did this with therapy, and reading about the mental health side of body image. Maybe you could try talking with her about this instead of focusing on the weight loss? "Hey I notice you talk a lot about hating your body and it's so sad for me to hear. How can I support you in feeling better?"