River makes my flush, but also pairs the board

[mustardo]

The problem is what can he possibly put you on? Are you really going to be bluffing an empty side pot with a missed draw representing a river hand? You've bet out on the second six and the flush and he has said I don't care about either of those possibilities. At best you can hope he has a straight and puts you on three sixes. I don't think you are ahead 30% of the time unless you have a read to tell you that this guy is too stupid to recognise the value of his hands relative to the board and has misplayed his overpair.

As an aside I agree that I would definitely try to avoid this problem by check calling the river.