River play, top two pair sees flush draw hit

[jthegreat]

A situation that comes up often enough to warrant discussing.

I'm in MP last night with AQxx, flop is AQx with two clubs. I bet the pot and only the button calls. Turn is a blank, I pot, he calls. River completes the flush.

Knowing the button fairly well, I'm fairly sure he just had two pair calling down, but he could have just backed into a flush. Since I'm out of position, what's my play here? If I bet, he's probably going to raise either way (as I probably would). So should I just check/call? That seems like a really expensive line, but the only other option is to check/fold, which seems too weak.

What's the general strategy here when you're out of position and the river is a scare card?