1/2 - Correct to check behind on river scare card?

In a heads up situation, against a normal opponent without a real read who has check/called and an overpair to the board, is it correct to check behind when the flush card hits?

Perhaps this is too general a situation but I've been checking behind a lot for fear of being check raised and thinking that I save myself a bet if he's looking to check raise since there's a reasonable chance he won't call the river anyway if he doesn't make something.

Am I costing myself too many value bets on the river? A lot of these players will call down with a crappy pocket pair and two overs on the board.

Thoughts on this?