[Apathy]

Unarmed posted some excellent advice, I will just add one thing, your turn bet is far too small and could have something to do with the big check raise your facing here, so you have to call.

I do think the most likely holding for the opponent is 8-8 though.

If you want to bet the turn I think you should consider betting more, and if you want to bet the turn you can't lay down imo. There just isn't room post flop in a raised pot for a bet on two streets and a lay down except in special circumstances on party sngs. Like others have said there is no real compelling reason to bet the turn.

Note however if the board was idential with an ace instead of a king I would favour betting over checking, which may or may not be controversial to some.