3bet pot continuation bet? NL400

[ogdundar]

My image is TAG, slightly on the LAG side. Haven't got to showdown in any 3-bet
pots earlier on this table. Villain is 24/20 over 400 hands, he seems pretty good.

Is this always a cbet? I don't think my hand has any showdown value at all, I think
villain has a pair or AK here and got me beat always.

Does the situation change with AKo?

Texas Hold'em NL $2.00/$4.00
Hero is BTN ($585.80 in chips)
SB ($392.00 in chips)
BB ($80.00 in chips)
UTG ($668.20 in chips)
Villain ($372.70 in chips)
SB: Post SB $2.00
BB: Post BB $4.00
*** HOLE CARDS ***
Dealt to Hero [Kd Qd]
UTG: Fold
Villain: Raise $16.00
Hero: Raise $52.00
SB: Fold
BB: Fold
Villain: Call $36.00
*** FLOP *** [9h 10s 3h]
Villain: Check
Hero: ???