Also, you need to make sure that your goal weight is realistic for you. At 13, I would not enter into any type of restrictive dieting without your parents help. Making good healthy choices is the best way to have a long term healthy physique.
I agree with weight training but it must be mixed with a healthy amount (30 minutes daily) of cardio activity that increases your heart rate (where you can still talk but are breathing hard).
good luck and talk to your mom/dad!
Make sure you do strength training exercises, as those build muscle (you won't bulk up) and muscle is what burns fat.
Lastly it takes 3500 calories burnt through diet and exercise to lose a pound. If you are doing all of this and still nothing go to your doctor and dietician. Sometime medical issues can prevent weight loss and the professionals can help figure out you are not losing anymore weight. As well as do a proper bmi etcetera.
Thirdly you can't get rid of the fat if you are not flushing it out. Drink at least 8 glasses of water a day and eat 25 grams of natural fiber a day. Switch to whole grains, apples and pears instead of berries,melons and bannas and brown rice instead of white. This helps to move food along better and flush pounds.
Secondly look at what exercise you are doing and up the intensity. For example go from walking to bike riding. Basically make sure you have more cardiovascular type exercises than muscle toning ones. When you hit the weight loss wall for dieting you often have to supplement it with exercise. Always go for the most active of exercises.
Losing weight is different for every person but there are some things you can try. First off if you eat less than 1200 calories a day you body may kick into starvation mode and that makes losing those last pesky pounds difficult because your body will desperately hold onto everything you eat.
Try to cut out bread completely. Im talking NO bread. I did this (im also 13) and I lost 0.7 kg extra a week.
Hope this helps, it helped me! :)