villain 44/27, 50 hands
FCbet: 2/6
Agg% F/T/R: 19/25/25

Prima, $0.05/$0.10 No Limit Hold'em Cash, 3 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $10.59 (105.9 bb)
Hero (BB): $15.88 (158.8 bb)
BTN: $11.24 (112.4 bb)

Preflop: Hero is BB with A K
BTN raises to $0.30, SB folds, Hero raises to $1.05, BTN calls $0.75

Flop: ($2.15) 3 8 J (2 players)
Hero ?

I have been battling with this guy a little bit on a former 3handed table slowly filling up. I've seen some fishy moves like a weird turn merge bet and a preflop 3b call with K2s BTN vs BB. I'm assuming at this point he's quite fishy and a little stationy. His aggression stats are somewhat contradictory to our history because he has been stabbing flop or turn in basically 4 of 4 occasions when I gave him the opportunity as PFA.
That's why I'm a quite unsure about how to play this on the flop. Betting certainly has merit because I can bet quite small and dictate the price. I don't expect him to fold much though and continuing betting on clubs or a Q doesn't seem super attractive vs this guy. I can also x/c but it will be tough to win unimproved if two bets go in on any 2 streets. Thoughts?