If we do weight training, does the body body burn the extra fats and use it as energy for the muscles?

Kind of.... Not while you are working out. Adding lean muscle will increase you metabolism. In fact, for every pound of lean muscle you gain, you burn 69 extra kcal per day. Unless you are working out extremely hard (using all your stored sugar) or in the morning before eating, you won't really utilize fat for energy (you'll use protein first).