How much should I weigh, if I'm a 16 year old girl, who is 5'8" athlete?

Depends. There are a lot of ways to answer this and none are perfect. I will use the nih's bmi calculator to suggest a range of weights. the range of suggested normal bmi is 18.5-25. At 5'8, a bmi of 18.5 is 122 pounds and a bmi of 25 is 164-1/2 pounds. Other factors matter, too, but that is a good range to start understanding normal weight.