My puppy is 12 weeks old and 4.5 pounds and the doctor said that is normal. After that I took her back 3 days later and she had gained weight (went up to 4.8 pounds in 3 days) and the doctor frowned at that when she got off the scale and the way he said "she has gained weight" made me realize she was gaining weight too fast and I know what I was doing wrong, I was feeding her TOO MUCH but he didn't say anything to me about it being bad but I could read his expression I was feeding her like 2 cups of dog food a day but I didn't know no better now I feed her 1/4 a cup of purina one twice a day or what ever she will eat of that and no more. She was 4.8 pounds last week now she is 4.5 pounds again which the doctor said is VERY NORMAL no worries. Talk to your vet for sure about this though to be safe!!
also shih tus gain weight EASILY and You can tell if you have a FAT shih tzu I could and now she is not so wide but healthy and I go by the feeding instructions on the food bag.