Villain is very tight. 15/13 and 3betting 6,7% over only 96 hands. For squeezing OOP here his range is very tight I'd say. good AA, premium KK and high rundowns. 

Flop: We can discount AA from his range since just called my 4bet pre. Since he will fold quite a bit or even all KK vs the 4bet (he shouldn't expect me to 4bet more than AA here pre) so he is suuuuper rundown heavy and therefore smashes this board.
How do we proceed here? Can I b/f small here? The only problem I have with it is that folding vs NFD (+gutter) or wraps would be terrible. On the other hand shoving or bet/calling here vs such a nit seems simply dumb. 
I could check back because I don't expect him to get too bluffy vs it but I don't want to give freecards to FDs and SDs. 
I'm really lost here. Help!

Also, how do we play this spot vs a villain with a wider squeezing- and then floprange?