Facing a river check after heavy turn action

[Chris Daddy Cool]

You're sitting in a pretty aggressive mid-high stakes game (30/60+ online 100/200+ live). You're headsup in a pot with position and your opponent just bet-3-bet you or checkraised you on the turn and then checks a blankish river. How often are you value betting a weakish made hand here like top pair weak kicker or second pair strong kicker? How often will you bluff a missed draw? And finally, what type of hand do you put your opponent on given his line?

Two examples would be something like
You have KJ on JT842 board maybe with a flush draw or two.

Or if you held K8 on a 84332 board.