AQs Paired board, Nut flush and two overs

Hi all. I'm playing in a hand and don't know if the player is floating me or not. I was multi-tabling and the guy had just sat down.

Scenerio:

Hand: AhQh
Position: CO
Game: NL50

Everyone folded to me and I raised to $1.75. The BB called. The pot now has $3.75.

Flop comes Jh 8c 2h.

He checks and I bet $2.75. He thinks a second and calls. The pot now has $9.25.

The turn comes the 8s.

Now, I only have Ace high really but I do (if he doesn't have a set or just made trips) have 15 out or I have 9. I'm wondering if the best play here is to bet the turn as well or to check and take a free card and evaluate the hand on the river?

Most people don't float oop. So assume he either has a J or an 8, and he's not folding any of those.. Take the free card.

I would rather bet if Villain was in position (more likely he called with just a medium PP).

Check and take the free card. If you hit your flush raise him if he bets or else bet yourself if he checks. Otherwise you are done with the hand.