flush card on river, villain leads into my set

Villain was 35/11 over 80 hands. This happened while 8-tabling so I didn't have much of a read on him except for the betting pattern. The main hand I feared was an ace + flush draw that got there on the river but I would think that most people would play a top pair + fd harder than he did. Then when it hits he makes a massive overbet and I called thinking there was no way he would chase a lower flush that hard. Should I have folded and gotten out cheap or paid to see it?

edit - i have $581 and he covers

Party Poker
No Limit Holdem Ring game
Blinds: $3/$6
6 players
Converter

Pre-flop: (6 players) Hero is UTG+1 with K K
UTG folds, Hero raises to $24, 3 folds, BB calls.

Flop: A 9 K ($51, 2 players)
BB checks, Hero bets $42, BB calls.

Turn: 2 ($135, 2 players)
BB checks, Hero bets $85, BB calls.

River: 7 ($305, 2 players)
BB bets $425, Hero calls.

Results:
Final pot: $1155

Ugh, what a gross river. It's a very frustrating lay-down seeing as he obviously didn't even have the Adxd that would've likely reraised that flop turn. I think I call this river read-dependant (If I think he's capable of making plays) enough, but we don't beat anything but a bluff. Nothing else is possible, he didn't slowplay a lower set or AK or blah, gross hand. At least the overbet lets you get away from it BUT the overbet is so suspicious, but it's probably just a tool that thinks you're gonna pay him off no matter what the bet. The problem is if you call this bet, you indeed were giving him the right odds to chase his small flush.

More I think of it, more it's a fold.

bet more on turn, gotta fold the river

bet 135$ the turn