How much should a 21 year old 175cm female weigh?

57-76 kg. Upon reaching adulthood, we don't take age or gender into account when determining appropriate weight, just height. Check out http://www.nhlbi.nih.gov/health/educational/lose_wt/BMI/bmicalc.htm to calculate body mass index (BMI). Normal is 18.5-24.9 while overweight is 25-29.9 & obese is 30+. However, this is just a starting point. Body fat percentage is even more important: don't be skinny fat.