Puppy dog eyes and drooling tongue  

Probably the most relevant question is: How old are they? lol If they are still young (16ish) then it's probably perfectly normal! =) Any older and it's starting to get maybe a little strange!

Does your granddaughter have a problem with it?

For me it is not normal and I would send him home. Date is date, but it is a limit with everything. He is very controlling and maybe obsessive.

Do not worry!!
This will only last for a short period.
Believe me , he will change.

Personally such behaviour worries me. Questions such as "Will he be able to take it if your granddaughter wishes to end this relationship one day?" and "Will he harm her and himself then if that day comes?" He seems to be overly possesive and a very jealous person. If he does not widen his own circle of friends, it's unlikely that he'll change his personality.