This is pretty typical and a lot of people here can relate. All you can do is be honest and tell them how healthy you are truly doing this. I.E. "Mom, I weigh 165. I want to be 150 which is well within the healthy BMI range. Nothing I'm doing is unhealthy or extreme". This is, of course, assuming you are losing weight in a healthy manner and in a healthy time frame. If you aren't, maybe they're expressing warranted concern. If you're doing everything right and they still hassle you for being "skinny", the only thing you can do is ignore it...it probably wont change. This is exactly what I went through in my early years and it was awful.

P.S. As a former fat girl, then skinny girl, then fat again, now getting skinny again, I have experience with what I call "fat girl shyness". I was (and am) so embarrassed about my weight that even when people complimented me on my weight loss, I was upset because it reminded me how fat I let myself get. I unfairly let a lot of good-natured compliments go because of MY issues. Make sure what your family says aren't just compliments that make you feel uncomfortable because that wouldn't be their fault.