When he checks the turn, I'm making a bet... now i know you are thinking, no, I wanna give him chance to catch up, but why not value bet here... if he's folding to a value bet, then he's not calling your river value bet either, as he's clearly afraid you may have just hit the flush..or, he thinks he's trapping you with his 2 pair or set or whatever, either way, i'd value bet and see what he does. Also, if a 4th spade comes on the river, it's never good for you, he's either then even more scared of the flush, or maybe he has the K.
Just my opinion, I can understand if youre first to act, check raising here, (ie, hoping he bets), but if he checks, why give him chance to catch a 4th spade if he's holding Ks...
But, on the river, as played, no, I'm not folding...