I think potting the turn and river out of position is a little extreme. He's already called your flop check raise indicating he has at least top pair. I would go maybe $4 on the turn, not sure about the river if he calls that. Depends on the opponent really, how likely is it that he has AJ, AT, A9? The guy minraised a limper preflop, minbet the flop, called a check raise, then called the turn when you potted it. I would slow down on the river for sure, unless this guy is an uber-fish.

AK sucks out of position - top pair type hands are so hard to play in this spot.