Wherein I cap the turn but check behind on the river

[sweetjazz]

This comes from a hand I played HU versus a villain who was new so I didn't have much of a read, except that in his first few hands he wasn't a crazy maniac.

I'm in the SB (button), and I open raise T [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/club.gif[/img]. Villain in the BB calls.

Flop is 6 [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/spade.gif[/img]. The villain leads out with a bet, and I elect to call.

Turn is K [img]/images/graemlins/diamond.gif[/img]. Villain bets again, I raise, villain 3bets, I cap.

River is 4 [img]/images/graemlins/spade.gif[/img]. Villain checks, and I check behind.

Can the turn cap + river check behind ever be right? I don't think so, which means I either should have capped turn and bet river (my plan was to call a check/raise), or I should have called the 3bet on the turn and called a river bet UI. Which line do you prefer?

I explain my river check behind when I give results.