I want to improve my weight

What often happens to girls your age is that they suddenly get taller and not gain weight. Your body might be getting ready to mature and you will grow about 3-4 inches, your waist will slim out and your breasts and hips will go "pop". I think you should continue to eat healthy food (no junk, no soda} and keep active. If you still feel you are overweight this time next year, ask your family doctor or school nurse for a diet plan.

If you want, mix up the cardio a bit, e. g. walk or play frisbee (or, gasp!) do housework or run, bike, etc. because just doing one form of exercise is, as you've seen, not too terribly effective over the long term. That also helps to prevent boredom so you're more likely to stick with things.

Dunno about weights; I'd hold off on them until you get a chance to talk to your doctor. They're probably okay but you should be sure. But cardio should be fine so long as you don't overdo it.