I think he checks the flop behind with his QQ-JJ type hands, but he might call a delayed cbet with them and if he is straightforward he probably bets all his AK-AQ when you check.

On the downside, you take a chance by giving a free card to his one combo of flush draw or his 2-3 outers, and there are reverse implied odds for your hand when he hits.

As a sidenote, I tried for once to slowplay my aces yesterday in a BvB situation, and it horribly backfired when he hit trips on the turn...