5' 6" and 96 pounds?!?!?! My goodness! That IS insane!!!

I have a friend who is 5' 3'', and weighs 87 pounds. She THINKS she is at a proper weight. She ISN'T!!! Its so scary giving her a hug because I feel like I'm hugging a skeleton.........seriously. It feels like she's going to break! EVERYONE tells her she needs to gain weight.............EVERYONE. She doesn't understand. She keeps saying she doesn't want to EVER hit 100 pounds. She was once at my house along with several other friends, and we were trying to get her to understand that she NEEDS to eat well, and that what she is doing isn't good for her. All she did was insist she likes being thin and will try her best never to hit 100 pounds. *sigh* We all told her that was illogical. We are a pretty close group of friends, so we can tell her practically anything, without hesitating, and without her getting upset. Unfortunately, it DOESN'T work. I don't know how to advise you, but I must say 96 pounds at that height, doesn't sound healthy at all.