I guess I can speak up as someone who is taller and has what may seem like a low weight for my height. I don't want to be skinny, but I do want to be thin. However, my body frame and size has some constrictions- I will never be less than a D cup without surgical intervention, regardless of weight. I will also probably never be any smaller than an 8, MAYBE a 6, regardless of weight.
My goal weight now is in between 130 and 140, 135 seems ideal, which probably seems low to a lot of people. I'm not married to it, but I liked how my body felt at that size. I'm not aimign for a particular number, but a particular feel to my body, which I think will be at that weight. At 130-135, I usually wore an 11 an juniors, frequently a 13. I was also a competitive soccer player and an avid weightlifter. At that weight, I could leg press more than twice my own weight. (I actually got used as a motivational weight lifting example for my college football team, followed with a "how come this girl who weighs 100 pounds less than you can press almost 100 pounds more than some of you?" Very proud moment for me

) So, yes, the number sounds low. But, on my body, it most likely looks very different than what you would expect it to look like.
With that said, I would love to be tiny. I would love to be a size 2. Never goign to happen. Plus, I never want to look weak or sickly. I would however, like to be thin, athletic, strong, and toned again.