What's do you think a healthy weight for a 15 year old girl 5'7 is??

According to BMI charts, anywhere from 120 to 150. Maybe strive for a middle area like 130-140. However it really just depends on your body type and what weight looks healthiest on you.

What does not eating more calories than you burn mean? I heard it's not healthy and I also heard that it's the best way to lose weight

Whoever told you it was “unhealthy” THROW THAT MESS OUT OF THE WINDOW!! Of course you don’t want to STARVE yourself! (We must always nourish our bodies properly. Of course a MAJOR calorie deficit is not healthy, but calorie deficits should NEVER be EXTREME) 

Losing weight is a simple mathematical formula: You need to burn more calories than you eat. Experts generally recommend creating a deficit of 500 calories per day through a combination of eating fewer calories and increasing physical activity. Over the course of a week, this should yield a loss of about 1-2 pounds of fat.” -WebMD feature

Honestly, it is really pure common sense. 

  1. If you eat more calories than you burn you will gain weight.
  2. If you burn more calories than you eat you will lose weight.
  3. If you eat the same amount of calories that you burn your weight will not change.

Another way to explain is to burn more calories than you use in 1 day. Your body uses so many calories to keep itself alive. Your body is always burning at least some minimum amount of calories that are used to support the function of vital organs like your heart, brain, nervous system, lungs, kidneys, liver, muscles, and skin. This rate of calorie burn is called your basal metabolic rate. If you want to accomplish anything beyond simply staying alive, such as losing weight for example, you will have to burn extra calories to do it. 

BMR Example:

Female:  Kahli

Height: 5’5”

Weight: 145 lbs

Age: 21

BMR (how many calories burned if she stays in bed all day): 1492.55.

So this means if Kahli does absolutely nothing all day, no activity no nothing, her body will burn 1492.55 calories. Now, If Kahli eats 3 meals that equal about 2,000 calories and still does nothing but lay in bed, she now has 2,000 extra calories that her body has no use for. Calories that the body DOES NOT USE are stored in fat cells to be used at a later date if needed = WEIGHT GAIN if Kahli stays sedentary.