How can I get more value?

Hand wouldn't convert, so here is the raw history. My only notes on this guy are from limit holdem, and they say he seems weak tight and that he shuts down on big bet streets. This could either be because he's a conservative player in general, or just that he sucks at limit, or both.

PokerStars Game #12020099497: Hold'em No Limit ($1/$2) - 2007/09/12 - 16:32:04 (ET)
Table 'Sophia V' 6-max Seat #4 is the button
Seat 1: aces&chips ($130.85 in chips)
Seat 2: realyleaky ($60 in chips)
Seat 3: Dr.kwan ($77.90 in chips)
Seat 4: dsaxton ($224.25 in chips)
Seat 5: DivisnByZero ($379.85 in chips)
DivisnByZero: posts small blind $1
aces&chips: posts big blind $2
*** HOLE CARDS ***
Dealt to dsaxton [Kc Kh]
realyleaky: calls $2
Dr.kwan: folds
dsaxton: raises $6 to $8
planet34 joins the table at seat #6
DivisnByZero: raises $22 to $30
aces&chips: folds
realyleaky: folds
dsaxton: calls $22
*** FLOP *** [Qc Jc Ts]
DivisnByZero: checks
dsaxton: checks
*** TURN *** [Qc Jc Ts] [6h]
DivisnByZero: checks
dsaxton: ?

Wait for an A to drop and hit it. Seriously, you are beat by every normal 3bet hand but AQ here. Play it down cheap.

I'd bet. He's pretty much telling you you're beating him. I'd even bet the river for value on a blank probably.

I'm guessing you don't think AK slow plays 2 streets here. Probably not, but if we're beating him what calls our bet? I am more likely to check this down if the opponent is capable of chk, chk. Chk, chk. Chk, chk. The read says he is passive on turn/riv.

i check it down like a wuss cuz you re beat here a humongous % of time by AA

The flop check was a hedging slow-play of sorts (trying to maximize against the weaker hands in his range while minimizing losses against the stronger hands in his range) which I'm pretty sure was correct. On the turn I felt my hand was good probably 85% of the time, but couldn't see any value in betting against his range. Regardless, checking twice seemed a bit ridiculous, so I decided to bet $45.