What's a healthy weight?

I'm a girl, 5'8, and I'm 16. I'm super skinny, like btwn 104 and 109 lbs (according to my Wii fit, i don't know how accurate it is though). I got blood taken and the results showed that I'm healthy so I don't think Im malnourished. But people think Im anorexic when food is like, my best friend. Since I was about 14 my appetite has slowly decreased but the Dr. didn't really find anything wrong with me and said I was healthy. Why am I so skinny? I don't play any regular sports, but I do snowboard and do water sports and such. I'm outside all the time. Can you think of any reason why my appetite is so small? I'm very confident in my looks and not very self conscious at all so I'm definitely not anorexic And what's a healthy weight for the average person with my attributes?