obviously 3bet bigger, to something more like $1 I think is good OOP and not closing the preflop action.

I don't think it's a given to Cbet this flop, it's ok to check this flop, however I am more likely to check if I am in position and checked to, then check behind for pot control. So C-betting is OK, but the board is really wet so when you do C-bet, the sizing needs to be bigger on the flop. I know it's a 3-bet pot so you don't have to cbet as much to get folds on cbet bluffs, but it's wet. And my plan for the hand would be bet/fold, if he flats, give up unless we improve on the turn.

The turn makes the board even wetter, and his range at 14/9 is very strong so just check/fold your AK