[Iconoclastic]

Against an average opponent I would Half pot bet on the Turn and check down River and call a 1/2 pot bet on River. However...

Will a thinking TAG call a Flop raise with KQ on a draw heavy board??? I doubt it.

With a set he would reraise the Flop to kick draws out.

The way it was played highly suggests flush draw- semibluff then calling with implied odds.

Which dictates check down.