Also, you're still growing and hitting puberty, so I would not have been really worried about the weight. Since you're young, your metabolism is fast, so as long as you exercise on daily bases, you should be fine.
Also, try to watch what you eat, meaning, don't eat a lot of fried food.
I suggest playing soccer, swimming, cycling, running or simply walking every single day.
I agree that since you are not fully developed, you should probably not worry too much, because chances are, you will taller and will slim down.
Per slocerberus, be sure to eat healthy; lots of veggies, lean protein, whole grains, etc. Avoid fried foods and junk foods such as candy, pastries, chips, etc.
Any type of exercise is good, so long as you enjoy it and do it regularly.
59 kg is 130 lb. There are many factors, but one chart suggests if you are 5'4" or 5'5", that could be an ideal weight.
The charts don't mention that some people have bigger, denser bones, longer or shorter legs by proportion, and more or less muscle.
Looking good and being healthy is more about having muscle and having a strong heart and effective lungs. To feel good and turn heads, WORK OUT. Eat lots of vegetables and fruit and lean meat and rarely take sweet drinks.