She is so sensitive, what should I do?

I started hanging out with this girl this year and she's really nice. I met her through one of my best friends at lunch and we just hit it off. Well now shes kind of getting annoying now, and when I say annoying I mean she is too sensitive. My friends and I love to laugh and have fun, we make jokes about eachother and laugh at ourselves. But anyways today my friends made a joke how we eat and stuff, she made a joke about Jammie( the girl I met this year) about how she doesn't eat alot, she never really eats. It was funny an we all laughed but she just rolled her eyes as always and stormed off. I always have to go and ask her what's wrong all I get is nothing. Don't say she doesn't like being made fun of or you guys need to be nicer blah blah blah, she already knew how I was and how we all act so I'm not changing how i act or my friends. We are all annoyed she gets upset over little things, so what should I say to her I don't want it to be awkward because they don't want to hang out with her. Im the only one who has probably gotten the closes to her, I don't want to stop talking to her but I'm sick of walking on eggshells trying not to say or do the wrong thing. So what should I do?