You may be a sore spot for her. She may feel resentment that you were able to lose weight. That doesn't make her a bad person, it's just where she's at. And it's not personal. I would suggest that you try to stay away from her. She may not want you constantly reminding her that she CAN do it, you may very well make her uncomfortable. Don't worry about her so much, just do you. Be positive, offer encouragement if she asks you for it but generally avoid her.
"Binging is a descent into a world where every restriction... is cut loose. At its core is a feeling of deprivation.. a feeling you can never get enough. Binges do not signify a lack of willpower or inability to care for yourself. On the contrary, binges are a urgent attempt to care for yourself when you feel uncared for. They are the voice of survival. Binges are the mark of the self that says, 'I am tired of feeling deprived, of being told I am wrong, that I am bad." - Geneen Roth