Don´t think you´re going to check behind there with 89, so if you´re going to c-bet with your whole range I think you should c-bet with KK for value, some players would often call with gutshots or lower pp-s.
I´d likely bet 1/2 potsize bet on the turn and then check behind river
As played: folding river is likely better, because he has there Ax or better hand a lot of times.