[Berge20]

CO posted and checked when it folded to him. I guess it is possible this villian just checked two eights there, but I'd be very surprised. (Wonder what his steal rate is)

Given that, I probably 3-bet the flop here. He has Kx spades often enough or K8/T8 to justify that raise.
Turn card is obviously not a great one--I almost want to lead 2/3-3/4 pot to see how he reacts, especially if you are check-calling such an amount.

His river bet is odd, but it could easily be the flush semi-scared of the paired card...but not wanting a free SD since you checked.