webwiller

Preflop why you 3bet? Is it for value? If yes than you should really believe villain would call you with almost any Ax, at least A9+ and all Ax's. If it's a bluff 3bet, I'd make it a bit larger to discourage an IP call.
Flop is tricky. Fortunately you have the Ac which is big thing on this flop with given action. Villain has no more al Ax's (not the right suit at least) and chances he would not let his top-pair go at first glance. He has AQ-A9 plus evey Ax's (of the wrong suit that adds-up 16combos of Axs we beat, plus 8combos of A9o we beat. 24combos)
What would villain do preflop with KJ-K9? Suited or not? If he won't fold these to 3bets...all Kxc have lots of equity agains us (plus position!) .
You're line...I like that. It tends to be interpreted as week (and I ask myself...is this your feeling about your holding?! "I'm weak, I check") Are you x/c or x/f the turn?!
I was saying...I like the b/x...but I'd better bet out the river than face a bet checking and finding myself leveling about me acting weak and inducing bluffs or even valuebets by worse Ax. I'd put out a 1/2psb on the river, even less, like 40%psb and hope to get a call by Ax and Qx.
MY line: b/x (a xf here) bet (smallish - a bf here)
River clubs put us behind some part of his range, but being a small card, puts us ahead of lots of his Ax and does not scare us a lot about lucky 2p rivered by villain.

After this "chatting" consideration, let's put down some math:

Standing on the preflo examination, I believe that hero's 55% equity is the very bare minimum for proceding in this hand.

Lets move on to the flop:

Don't misread: I've assigned a weight to some combos. If you're not familiar with flopzilla I've assigned that villain would "trap" with QQ 10% of the times, with KK, 15%, and AA 20% of the times. Normally your 3bet range from SBvsLP should be high enough to justify a fairly decent trapping range.
In any case we got 60% equity now, and many cards that would scare us. But yeah, your betting is +EV on the flop. I noticed just now your size. GOD. 1/3psb on THIS flop?! To achieve what? You almost never get a fold. When you get called you won't know any better villains range. You let drawing hands draw correctly having perfect odds. And you get the smallest value from the hands you're ahead now, with high probability to be bluffed off your hand and letting them too drawing to a better hand (Ax can make 2p, A2s goes ahead on turn paying the right price) You have to make your villains make mistakes, not play perfectly agains you! Anyway...getting to the turn...

As said...you loose 2% equity because of few hand making a better holding at a bargain price!
But lets get to....

The River
Now we have to establish which part of villains range would bet out on this river and therefor decide if we have a profitable call here on average or if we are making donation to our poker population. On the flop, nothing of villain range would fold BUT on the turn a part of villains range would bet 90% of the times, and that part of his range is no longer with us. We have to make our best educated guess on what this part would be and see how we do with the rest of it that would fit this action.
Lets see, after taking out what villains would donk on the turn, and taking out what he'd just check back on the river what we're left with:

As you can see, your hand is best 90% of the times, so you have a mandatory call here. Said that, Id change my line:
b/xf/xc
What I'd suggest is: folding preflop would make your life a lot easier. Second, why not making your hand review and comparing it with others. 3d, try to provide some genearl infos, like some basic stats of both hero and villain, forseen images of players involved. Last but not least: post less hands but more in depth. This will make you grow easier and faster! gl@the tables man!

The easy way to answer your post without all this work of examination?!?!

FOLD PRE.

LOL.

ww.

I won't bother balancing at these stakes unless I'm 100% sure villains watch out and exploits me for not balancing. I believe balancing matter is overvalued at these stakes.

b/b/bf
preflop I'd sqz a bit smaller, about $2,10, I make 1/2pot cb, bet 1/2pot turn and 1/3pot river and fold to turn/river raises. A lot he could pay from behind, this justifies the betting pattern, not much at all he'd bluff with on this turn/river, therefore the b/f.

You cannot say you got room to call river on the assumption that anonymous villain will always push river with all of his busted draws, many of which won't even be there standing on the preflop action imho. I don't dislike the flop size as we have many TT-JJ in his preflop calling range. On the river hero beats bluffs only, and I don't think you have enough bluffs without history in this spot, especially in a 4bet pot with an OOP Villain shoving over you.
I went through the hand with flopzilla and imho, you are giving villain a very wide range considering that he is flatting a cold 4bet OOP. I put 15% of trapping with AA-KK, I put 99-QQ, AKs, AQs, KQs. If you consider that TT-KK, AKs, AQs won't shove over you for obvious reasons you remain with a very rare set A's, set of 9's and the only combo that might go through all this and decide to bluff the river with no sd value to make you fold just right the hand you hold might be KcQc but it won't be enough for a profitable call.

You might consider it weak but at these stakes I'd rather cbet flop and bet/fold turn to take value from Ax (mainly AJ-AQ) but I don't see anything worse that would raise this turn and don't believe he has that many bluffs on this board too. I expect villain to have a value hand that beats us most times. He could cold call preflop with A8s, ATs, 78s, 88, J9s and other Ax that we beat, or big pairs that would call one, I see hard to turn them to bluffs on this board.