Why does my friend always put me down, but she herself is very sensitive?

My friend puts me down in the form of "jokes" or just sometimes outright put-downs. She keeps talking about my height because I'm quite short (5'4) and says I'm "too skinny and need to eat something." She also joked that I'm dumb/stupid. The one time I got annoyed at her, she told me I'm being too sensitive and can't take a joke. Then I said that because we're the same height, she must also be short then. I wanted to give her a taste of her own medicine. She then got extremely offended and told me to "f*** off." She gets extremely touchy with even perceived slights where I didn't mean to offend.

Why is she so touchy with put-downs when she always puts me and others down?

Why does my friend always put me down, but she herself is very sensitive?
Post Opinion