Alright well you should be eating around 2,500+ calories a day. Along with that you should be working out and excercising. Aslong as you consume 500+ calories a day than you burn you'll start gaining weight. It takes 3,500 more calories than the calories you burn in a day to gain 1lb. If it seems like it's taking too long eat more but if you start to see yourself developing a gut then ease down a bit. Oh, and don't be downing burgers and fries and all that junk. You also have to eat healthy! Foods high in protein and low in fat will help (chicken breast, salmon, tuna, egg whites, etc)
My son is 12 years old, 5-1 and 82 lbs. He is VERY skinny. I have him eat everything, anything he wants. Cici's, hambergers and fries, Taco Bell. He stays the same weight. The Dr even says he needs to eat more and gain weight.