Can A Full Grown Shih Tzu Weigh 7lb?

Yes, they are called imperial shih tzus. Mine is 7 and a half pounds full grown. It is not unhealthy. They are the smaller "petite" shih tzu and perfectly fine.

If you have one then they can.  The question should be: Should a full grown Shih Tzu weigh 7lbs.
The standard is 9-16 lbs with a full coat and 9 - 10.5 inches tall.  A lot of people have 11 inch or taller Shih Tzu that weigh more then 16lbs with their hair short and then like to make people with the correct size feel bad.  Your dog is a little small for standards but a 11" tall 16lbs short haired Shih Tzu is large and most likely cross breed.  Make certain with your vet that it is healthy.  If it is under a year old it will still fill out and gain some weight but the height does not change much after six months.  People should check standards before they tell you your dog is unhealthy.  Let your vet tell you that.  Good luck they are great dogs I have been raising them for 20 years.

Yes, My Shih Tzu is 7lbs fully grown, She was one of 7 and the smallest in the litter by far. She was one of the healthiest and strongest of all the pups and has never been sick, She is just a tiny Shih Tzu. 

People are often too quick to judge that if your Shih Tzu is very small then they are unhealthy? Not true! Some tiny ones may be unhealthy as some larger Shih Tzus can be unhealthy, But out of my 3 Shih Tzus our tiny girl has been the most active and healthy. You can't say someones dog is unhealthy just based on its size -  that's ridiculous!