Eating sensibly is not going to stunt your growth, in fact the opposite is true. If anything, making sue that what you eat is healthy, nutritious and good for you will help your body achieve it's full potential.
If you have a family doctor, it might be an idea to ask your Mom to take you to see him/her so you can discuss this. A doctor will be able to give your parents impartal advice on whether your weight is an issue and maybe even give you a plan to work to.