It seems like he cares about this girl, just not in a romantic way and he does not want to pursue a friendship. That doesn't mean you don't care. I agree that you should stick to aquaintances type "talk" and don't pursue a friendship with her. Definitely help her become friends with some women in the church, get involved in the women's ministry or other ministry there, so that she can start realizing that she needs to let God heal her and that following you around is not going to make you like her. It does seem that she is craving friendship....so talk to your female friends at church and ask them to include her in activities and to become friends with her. That's what she needs right now. Also, pray for her! I think most of the advice that has been given is good advice.
Oh, also I have a personal story about this. When I was in youth group I liked this guy there. He actually was not the most popular guy and he was not the nicest to me, but I still liked him. Probably because I wanted to fit in. I was even more overweight than I am now and I did not wear cute clothes, I was not a cheerleader, I had low self esteem , etc. So, for probably many reasons, he did not want to date me. I tried to build a friendship with him, hoping he would see how great I am (lol) and start wanting to date me, but he always pursued other girls in the group, never me. Not only that but he actually treated me differently than the other girls, in a negative way. He would often ignore me or act like I was not good enough to join in on an activity. On a ski trip once, one of the guys that was in his "ski group" asked me to join them to ski some blue runs because I didn't have anyone to ski with and we were not supposed to ski alone. I accepted the offer because I knew my youth pastor would be upset if I skied alone. The girls in the group and most of the guys were nice to me, but this guy that I liked was awful. He kept trying to leave me behind! Talk about disliking someone! He was trying to get the group to leave me behind...lol. I'm not even a loud person or anything like that, quite the opposite, which may be why he didn't like me who knows. ANYWAY, I know how it feels to be the one who is not liked, so be kind to this girl and don't do things intentionally to say "hey I don't like you at all"