If YOU are the one unhappy about it, then do something to change it. You're 13, and 60kg. Assuming you're short, you might be at risk for illnesses and diseases related to obesity in the future. If you feel that you need to lose weight, do it. Its your future. Regarding what everyone says, i understand. Whenever someone calls me fat and all i too, get upset and feel like punching them. e___e in you're title, you said that you feel like you need to lose weight. In that case, Do it.
If you want, start of by eating healthy. Cut out unhealthy food from your diet slowly. Start by stop buying sweets, chips and fast food. I recommend you do at least 2-3 workout regimes from this app everyday, at least four to five times per week.
If not, go jog :3
For food, if you crave for sweets and chips, try making alternatives. Try making sure that everything you eat are home made. If you want a snack, make it yourself. If you don't want to make your own chocolate bars and potato chips, opt for an apple or a different fruit. But if you want, you can make your own bland popcorn :3
If you want, search for blogilates on youtube. She's a pilates instructer with fun workouts that you can attempt. :3 and for more advice, Go to 10000steps.tumblr.com (Not sure how many zeros there are in the url. But you can google that up :3)
Hope this will help you<3
A lot of the times teens gain weight right before they gain the height at puberty. My brother, and I did. Personally I'd just try to eat healthier and not worry too much about it til later in life.