I'm trying to figure out heads-up play in a full ring game, particularly when I'm OOP. Here's a 2/4 hand from PokerRoom. Comments on the check-raise as well as PF is appreciated. I just called the raise to keep the BB in, as I figure I'm OOP anyways, so why not pad the pot w/ a premium hand. Is this good? Or best to just try to get it HU right off the bat (he didn't call, so it doesn't matter w/ the action).

Hero [ AH,KH ]

ANTES/BLINDS
Hero posts blind ($1), BB posts blind ($2).

PRE-FLOP
2 folds, Villain bets $4, 2 folds, Hero calls $3, BB folds.

FLOP [board cards 7H,5S,9C ]
Hero checks, Villain bets $2, wrf1979 calls $2.

TURN [board cards 7H,5S,9C,9D ]
Hero checks, Vaillain bets $4, Hero bets $8, Vaillain folds.

I had no read on villain, as he was new to the table. I figured there was a good chance I was at worst chopping with him. When the 9 paired, I figured it was a good chance to bluff at it, although I may have been ahead anyways. On a side note, one thing that made me think about slowing down a bit was that he when it was his turn PF, he seemed to have the RAISE option checked, as it was instant. Do you all consider this a strong tell, or pretty random? I know it could be either Raise to $4 (or w/e 2xBB is), or Raise Any, the latter which would obviously be a much stronger hand on average.
Anyways, on the line I took, I'd like comments on what I should do if he had done something other than fold. I figured I would fold to a 3-bet, or check/fold the river if he called then bet the river. Would a call-down be appropriate against an unknown in this situation?? Thx in advance.