KK on the turn

Hero has pocket kings utg with 15 bb behind. Raises pre flop, and gets called by the player directly to hero's left, as well as by the player in the bb. Flop comes J93 (two clubs), and the bb checks. Hero cbets 1/3rd of pot and is called by both players. Turn is Qh, bb checks, what should hero do? The example from episode 149 was playing in my head when I was in this spot, and I remembered the hero checked the turn instead of betting. So had I had more behind, I probably would have done that, but since I only had a 2/3rd sized pot bet left on the turn with an overpair to the board (which had no real draw presence with the exception K10 & T8 making a straight), I thought it was a better idea to shove here instead of check. Do you agree? Thanks