LIGHTER DOES NOT always MEAN FASTER. Instead of downgrading to a light and weak Prius, why wouldn't you go for a Ferrari?
Restricting calories to an unhealthy point, especially at this age, is dangerous and can promote further health problems down the line, such as a shortage of nutrients when your body is still in development that causes decreased bone density for the rest of your life. It's not worth it.
The proper progression goes something like this:
1) Get into the sport of running and find why you love it - for the competition, freedom, teammates, whatever it is that captures you specifically. Find a true, healthy passion for the sport.
2) Train hard, but don't make running your entire life and let it consume you completely.
3) After you've had some success in the sport and decide you want to pursue it more seriously, fine tune things little by little: better sleep, better training, better all around body strength, healthier food NOT less food. If you train right (including core and stability exercises and a small amount of weighted exercises) and eat healthy food without restricting calories you should see your body condition itself to it's own proper training weight. It may surprise you that it's possible to go up in weight. This happened to me... I gained 10 pounds and went from 15:00 to 14:10 in the 5k simply because I had more all around strength.
You should never lose weight as the first fix to getting faster. Your focus should be training hard and properly fueling your body with enough nutrients to recover. This topic needs to be handled with care. Good luck.