Would I lose weight if I became a vegan?

I'm 14, 5'4 and 93 pounds. I want to be a vegan because I have very strong feelings towards kiling animals. l don't like milk or eggs or cheese LOL. I eat tofu, tons of veggies, beans, lentils, nuts, bread rice and pasta (whole wheat only), fruit and soy. My parents won't let me because they think I'm too thin! How do I convince them?