I think your weight for your height is healthy. 125 is too low. Instead of trying to lose weight, maybe you could add some weight training to tone? You probably look great but don't even realize it. Being super skinny is not the way to go. Take care and good luck.
I like the "super skinny look" and have been there before at this height. 125 is not medically too low and I figure if I get there in a healthy manner, I should be fine. Though, I'm going to be doing more exercising this time around, so I might stop at 130, depending on how my clothes fit. I basically would like to fit into my size 3 jeans again.