Attempting to catch a bluff

Opp is 31/21/2.3 after ~100 hands. This just felt like a good spot to do this.

Party Poker No-Limit Hold'em, $ BB (5 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero ($50.25)
BB ($50)
UTG ($74.61)
MP ($84.15)
Button ($58.55)

Preflop: Hero is SB with A, K. Hero posts a blind of $0.25.
3 folds, Hero (poster) raises to $1.75, BB calls $1.50.

Flop: ($4) 6, 4, 4 (2 players)
Hero bets $3, BB calls $3.

Turn: ($10) 4 (2 players)
Hero checks, BB bets $6, Hero calls $6.

River: ($22) 9 (2 players)
Hero checks, BB bets $17, Hero calls $17.

Final Pot: $56

I probably wouldn't c-bet this flop. And I would guess he had some sort of pp here. His preflop stats are high but his aggro is only 2.3, which is not that big.

I think you've been had.
You only have put $5 in that pot. Fold it on turn unless you have a killer read that he will always bet into weakness. Any PP beats you along with A6, A4, 45. He also might call with a larger range since he may be defending his blind.

To the contrary, I cbet this flop everytime. The paired board makes it much harder for the opponent to call a bet without at least a PP.

I don't think this is the right flow for a bluff. They don't usually "take over" on your aggression to start bluffing. (or they'd atleast do it with a c/r) You can better pick off bluffs when they raise and (you suspect) cbet.