I can totally see and agree with what everyone says here but I guess I have to be a bit of the devil's advocate--if it's a marriage, then of course, you are bonded before God and are to see your partner through. But, seeing as you are not married...
Is this girl open to seeking help? I would suggest going to a trusted pastor or Christian counselor with her and discussing this problem together. If she is not willing to receive help, I would prayerfully consider whether or not you are meant to be in this relationship.
I completely understand what everyone is saying about supporting someone through such an incredibly difficult ordeal, BUT, people in such situations can also become even more unhealthy by clinging onto, becoming co-dependent upon, and looking to another person to heal them instead of God.
I say this for two reasons: I myself have struggled with symptoms for several years, but the doctors never felt I qualified for an "official" diagnosis. My husband once heard me retching in the bathroom and it was not a pleasant experience, for him or for me. Such cycles can become addictive... and sometimes there is nothing you can do for the other person. He chose to leave for a myriad of reasons, but in all honesty, God was trying to pry me away from my dependence on another person for my happiness and well-being.
I also feel that such cycles can be like other addictions--and sometimes it's unhealthy for the relationship to stay together. I was involved in a relationship with someone who had an addiction to alcohol and with two small children were involved, it was one of the hardest decisions of my life--and I chose to leave. As time has gone on, I know I made the right decision.
I am NOT trying to say that an eating disorder is the same as alcoholism--I'm just saying it can follow some of the same patterns, and since you are not married to this person, it truly may not be your calling to stay in the relationship with them. If God's will isn't for this relationship to continue, holding on will actually make it worse.
God bless you for being considerate of this person's needs but also being honest with yourself. The boyfriends I had were not the right relationships for me and though I hated being alone, having to be alone is part of what brought me to a place where I COULD get better from both eating disorder symptoms and cutting. There is no doubt that if I were still in one of these relationships, I would have never gotten better--even though it was hell at the time.