considering you think AA/KK would shove turn, then his line is the perfect way to play them against you.

I think that shoving here turns your hand into a bluff, I dont see what he could possibly call with that you beat that he didn't lead turn with.

He probably hasnt got a draw as I'm assuming he would bet the turn with it, so if he is behind he is drwaing to either 2 or 6 outs most likely so check and give him a chance to bluff you on the river if you think you are ahead.