Am I obligated to call down here?

[UMTerp]

Semi-common situation where I'm starting to question myself. This has happened to me 4 or 5 times over the past few days. Typical middish limits online game - 15/30 thru 50/100, solid/aggressive players.

Here's a hand from today. I pick up KsJs in the BB, hijack raises, CO 3-bets, I call(?).

Flop K82 rainbow. Checked to the raiser, I check-raise, we lose the player in between, and the CO calls, sometimes after a dramatic pause. I bet out the turn blank, get an instaraise behind me, and now what? I've been calling down, and I seem to be beat every single time (whether it be AA or AK or KQ or 88.)

Can I fold the river if he bets again? I mean what else can he have on that dry of a board? Or have I just been running bad? It seems weak to fold top pair in that spot, but I'm never ever good. Call the turn and try to spike a jack or hope he checks behind on the river? Help me out here.

Obviously it's an easy calldown if the preflop 3-bettor is semi-maniacal, but how about if he's just a 30/20 type?