To cbet or not to cbet?

[seven-deuce]

PokerStars No-Limit Hold'em, $0.05 BB (6 handed) - PokerStars Converter Tool from http://www.flopturnriver.com

MP ($10.24)
CO ($10.37)
Button ($3.93)
Hero (SB) ($9.98)
BB ($7.28)
UTG ($5.36)

Preflop: Hero is SB with A, K
3 folds, Button bets $0.15, Hero raises to $0.45, 1 fold, Button calls $0.30

Flop: ($0.95) 9, Q, J (2 players)
Hero checks, Button checks

Turn: ($0.95) 6 (2 players)
Hero checks, Button checks

River: ($0.95) 4 (2 players)
Hero checks, Button checks

Total pot: $0.95 | Rake: $0.04


Treat villain as unknown.

My preflop 3bet range in this spot is { A2s-A5s, AK, TT+ }

So i decided not to cbet this flop because i thought it hit his range pretty hard, i think he is going to have a lot of Qx Jx when he calls my 3bet preflop. So i didn't think i would have much fold equity on this board and also if he calls the flop there aren't to many turn cards i can barrel on the turn to get better to fold i don't think.

Like if i cbet the flop and he calls he's gonna have a Q or J alot of the time sometimes a pair and a draw with the T. So obviously i can barrel some turn cards with decent pot equity i don't think those cards mainly hearts are going to add any fold equity.

For example i stoved my hand vs a turn calling range with a heart turn card;

Text results appended to pokerstove.txt

1,848 games 0.001 secs 1,848,000 games/sec

Board: 9h Qc Js 4h
Dead:

equity win tie pots won pots tied
Hand 0: 32.089% 32.09% 00.00% 593 0.00 { AhKh }
Hand 1: 67.911% 67.91% 00.00% 1255 0.00 { KJs+, JTs, T9s, KJo+, QTo, JTo }

So i obviously have decent pot equity but all the hearts bar the Th which gives me the nuts and nut redraw are gonna give me any fold equity. So say he calls the flop with hand like KJ or KQ if a 5/6/7 of hearts hits the turn for example nothing has really changed and it's not like its a scare card for top or second pair that may have a straight draw to go along with it.

I suppose i can rep a set of jacks queens and KK AA.

Should i be cbetting here? Am i underestimating my fold equity here?