To gain some weight, he should stick with a healthy diet (not too much fried food, plenty of fruits/vegetables) and continue the exercise. Working with both a nutritionist (RD) and a trainer (coach) helps ensure the diet is appropriate and the exercise helps to achieve long term goals. Certainly plenty of calcium is necessary for growing bones, needed to support the extra weight being accumulated. Weight training, in particular weight lifting, is okay to begin at this age, but for the readers should not be instituted in younger children when their posture might be adversely affected. (see attached link)
If your son is underweight, if he eats a balanced diet and continues to exercise, he should do well. Again, assistance from a pediatric nutritionist can be essential to assure appropriate nutrient intake and weight gain.