villain 28/22 over 60 hands

Prima, $0.05/$0.10 No Limit Hold'em Cash, 5 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $10.37 (103.7 bb)
Hero (BB): $20.99 (209.9 bb)
MP: $9.80 (98 bb)
CO: $9.35 (93.5 bb)
BTN: $10.60 (106 bb)

Preflop: Hero is BB with A Q
2 folds, BTN raises to $0.20, SB folds, Hero raises to $0.80, BTN raises to $2.20, Hero calls $1.40

Flop: ($4.45) 8 3 A (2 players)
Hero checks, BTN bets $2.95, Hero calls $2.95

Turn: ($10.35) 9 (2 players)
Hero checks, BTN bets $5.45, Hero ?

Pre should be fairly std vs an unknown reggy player. When he bets so large on the flop, I'd say his range is strongly weighted towards value and draws he's going to shove the turn with. I expect a 2nd barrel close to 100% of the time. And this makes it quite uncomfortable because he can have AK, AA whereas I'll likely shove those pre 100% of the time. His bet is also too expensive to happily call flop and fold turn it seems. On the other hand however, this is the strongest hand I can show up with postflop, so if I fold this, I pretty much fold 100% of my range. How do you go about this spot? Maybe play a mixed strategy and call some % of AQ unblocking spades and explo fold the rest either on either street?