When to let go?

[hedgetop]

Here is a hand from memory it is vs a loose but slightly passive player who has played against me for a while on this table lets put them at 40/13/1.2 action is as follows

10/20 6-max Party Poker
Hero is dealt KK UTG

Preflop:
Hero raises, MP raises, CO folds, Button folds, SB folds, BB raises, Hero calls, MP calls

Flop:
973 rainbow
BB bets, Hero raises, MP calls, BB raises, Hero raises, MP folds, BB calls

Turn
Q offsuit
BB bets, Hero raises, BB raises, Hero Calls

River:
A offsuit
BB bets, Hero ...

I am pretty sure we are done once the river comes so I am pretty sure a fold is in order despite the pot size.

Once I was 3-bet on the turn I think his range is limited to a set, AA, KK and very minute possibility of AQ which I think we can basically write-off I know some would be opposed but is a fold on the turn conceivable?