What is normal weight and amount of food for an 8-1/2 mo old Shih Tzu?

Charlie has weighed 13 lbs for the past two months. Recently, he became ravenous and his food is gone by 11 AM - AND he's gained 2 lbs. He gets about 1-1/4 cups of dry food and free feeds. Am concerned about his health and getting too heavy. Also, my climate is cold so he isn't getting as much exercise tho I play with him inside and let him race around quite a bit. As an aside, I never thought he would be this big; the mother was 8 lbs and the male 14. HELP, would sure appreciate your ideas. I'm stumped. Thx. Kathy