Seriously? If you weighed 80 lbs. You'd be dead. Your ideal weight at 5'2'' would be 110 lbs., which doesn't take into account frame size, etc. For you, 120 may be perfect. Either way, DO NOT try to be under 110 lbs. By eating healthy foods and portions, and exercising three to five times per week (sports are a great way to do this), you will have a healthy weight for your frame. You are not fat. Stop thinking that way.
Source: My husband is a personal trainer and has various degrees in exercise. FYI, I am 5'2 and 120 lbs. As well and very healthy.
Eh...you could work out at least 3 times a week and cut out any "fatty" foods out of your food pattern. But that doesnt mean starve yourself. Start out easy on working out, like 10-20 minutes, and stretch a bit before so you wont pull a muscle. Once you feel comfortable, you could lenghten it a bit, but don't over exercise. You might get cramps on your feet, that happened to me when I exercised almost every day. They arent fun. =( You might start to gain some muscle too. Just be healthy as best as you can...talk to your parents and demand them to help you through this. Thats their job anyway. And don't skip any meals. I don't eat lunch at school, and I think that I'm starting to get unhealthy... I'm 13, 5'5 and the last time I checked, between 115-120 lbs.
When I was 12, I was 5'2 and 85 lbs. I was always rail thin as a child and had serious food issues in Middle School (basically I would live off fruits, vegetables and water). In no way was my weight ideal. People would actually call me anorexic and bulimic to my face (including teachers which resulted in me spending a lot of time in the principal's office trying to get them fired). I eventually decided to gain weight. Which since I was always small and I guess have a high metabolism was very hard. Now weight 120 with no effort, 115 with regular exercize, and I call this ideal. My advice, don't lose any weight. Instead, focus on healthy life choices.
I'm the same weight and height, and want to lose that same amount to be about 90 lbs. D: I think that I'm 5'3 now though. And I'm 124 lbs. D: Sooo fatty, but your probably not fat !