What is the ideal wieght for a high school sprinter who is of 5'7 in
height and 15 or 16 years old?

I'm not sure there's an actual number that I (or anyone else) can give
you.  So I would say that your ideal weight is that which makes you
fastest.  Here's what I mean:
Sprinting is, above all, a sport of strength, in particular lower body
strength.  Weight training and sprint-specific training should focus
on making your legs and core (abs, lower back) stronger and more
explosive.  With increased strength comes increased muscle mass and
therefore increased weight.  But since the weight is muscle, it will
very likely make you faster, in spite of being heavier.  So, to me,
the only thing that ultimately matters is if your times are coming
down, not your weight.
Of course, this argument assumes that your bodyweight is predominantly
muscle with a low body fat.
Hope this helps.  Let me know if this is not clear or you have other questions.
js

The weight you are now.  ;-)  Eat healthy.  Excercise. Don't screw up
your health while you're still growing without consulting a
nutritionist.

there is no such things as an ideal weight. everybody is different,
have different weight on their bone mass, different level of bodyfat
percentage, etc. as long as you are not especially thin or especially
fat, then i personally think you are normal! anything from 130 to 190
lbs sounds normal and healthy too me.

eat right, exercise and stay away from drugs and you will be in a good shape.