I'm kinda torn on what is the right thing to do on the turn here. I chose to bet fold; any thoughts on other lines? Villain is a fish with aggro tendencies, not an outright maniac though i.e. he is capable of bluffing and overvalues hands but does not attack everything blindly. I am not sure if his limping range includes Ax. I did see him open raise T5o and three barrel 7K8 Q 5 board, fwiw

Absolute/UB Cereus Hold'em, $10.00 BB (2 handed) - Absolute/UB Cereus Converter Tool from FlopTurnRiver.com

SB ($173.50)
Hero (BB) ($217)

Preflop: Hero is BB with K, 10
SB calls $2, Hero raises $10, SB calls $5

Flop: ($20) 4, 9, A (2 players)
Hero bets $5, SB calls $5

Turn: ($30) 3 (2 players)
Hero bets $10, SB raises to $20, Hero folds

Total pot: $50 | Rake: $0.50

if we folding to a raise why are we betting the turn?

because he is known to peel flops extremely light both IP and OOP and I want to charge godzillion of 6-outers he may have. I will be happy to hear counters for this reasoning, and PM is gladly accepted as well
If your question is always valid, then how you make bet folding play ever explainable ?

This sounds just like an opponent I've played on AP. If it is, he might be popping anything from middle pair to a flush draw or even a gutshot here.
I would probably check-call the turn for a several reasons: bluffable card, he's capable of limping an ace (depending on how I've played his limps previously), wtf could he have called the flop with, I want to see the river as cheap as possible w/ a decent king, and I have a hard time three-betting the turn with no pair and no draw.
Also, I really, really want to see his cards to get a better idea of his limp plays.
As played, the fold is probably correct. But it's important to know how you've played his limps previously. Some opponents never catch on even if you raise all their limps. Others try to get cute by limping monsters, and anything with an ace is a monster in HUHU, isn't it?
Please don't flame me if I'm dead wrong, or if I've prevented five would-be fishes from joining a HUHU table, but I thought I'd type some actual poker ideas, for all my fans who say I never do.

If I know he's able to 3-barrels with T-hi, I prefer c/c turn
Easy

At least we give him a chance to bluff, and it's very difficult to betting K-hi for value here (not impossible of course)

right, but it's much harder to do OOP, compared to inducing bluffs IP. OOP, once I call his turn I commit to calling pretty much any river, I have to be right that he's bluffing too often (I am basically given 2:5 odds, right?)...

Tough spot. Don't see a clear answer without more reads. As for the reason of charging him for six outers on the turn, wouldn't he be charging himself by bluffing the turn?

Had I more reads, I wouldn't be posting this hand....

This a difficult spot, becouse each play is possible bet/call, c/call, bet/fold

C/fold of course isn't possible imo

When I try to check/calldown in a spot like this I think I loose often on average, but I try to figure it out what my opponent is doing going at SD pretty light

Playing the check/calldown line I think is ok against loose peeler and aggressive at the same time: when we check they bet almost always on any board with
almost any 2

We can balance this with strong c/r turn

Not saying you didn't provide enough reads, I'm saying its a tough spot and I wouldn't know exactly what to do either.

Anyways, if hes an aggro fish, like I mentioned before, wouldn't he charge himself for most of his 6 outers?

Not that the post as a whole was bad advice, but I fail to understand why wanting to see what cards he is limping with factors into a decision between calling and folding. You don't know how long the match will last, and if it does last long, you will find out what he is limping with anyways.

U raise Kx preflop, he calls Axx flop and he is somewhat aggro and somewhat fishy. U dont want to put in 3BB more and u certainly have to much hand to fold. That leaves checkcall as ur best option. If he is stupid and overaggreissve betcall cold be fine. Betfold is fine if he is passive.