bet turn bigger, probably closer to .4; if he hit the k, hes probably going to call anyways, and youll be bolstering the pot for the river. this has the added benefit that it could potentially look like a fishy 2nd barrel, since if he put you on a vaguely tight range preflop, he might think youre being bluffy, and call with more gutshot type hands, or 2nd/3rd pairs.
as played, river checkraise to 2.2-2.4, giving him some room to shove over with tp type hands