Q: is it possible to add muscle to your legs through weight training while still playing sport and running often?

A: Definitely! The key to building muscle (besides weight training, of course) is eating enough to slowly gain weight. Playing sports will burn a whole lot of calories, so what you'll need to do is eat more and more until you start slowly gaining weight. It may take A LOT of food but it's certainly doable. Focus on calorie-dense foods like whole grains, brown rice, sweet potatoes, fruits, dry-roasted nuts and natural nut butter.