Keep betting?

[flair1239]

I agree with checking behind on the turn. If you are already beat it saves a bet. Giving a free card is of minimal concern, as another Ace does not beat you any worse, a King gives you a split (disregarding BDFD), also a fold from UTG is unlikely as most hands that he would cap with have hit the board and probably have additional outs, if he was slowplaying something nasty it saves a bet.

The river, in practice I am checking behind. There are more hands that he would cap with that are ahead then behind. The coordinated nature of the board, might be making him reluctant about betting AK or KK.