5nl FR: AKo misses flop, w/ confusing villain

[Ruosteinen]

Hero is a pretty new player with less than 1k hands total.
The only read on Villain (from around 20 hands) was that he's on the tight side of average - at least for .02/.04 - and folded to a couple of cbets earlier.

$ 5 USD NL Texas Hold'em
Seat 6 is the button

Seat 1: Hero ( $ 9.13 USD )
Seat 10: Villain ( $ 1.51 USD )

Dealt to Hero: K[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/heart.gif[/img]
1 fold, Villain calls $0.04, Hero raises to $0.20, 6 folds, Villain calls.

Flop: 3[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/club.gif[/img] 5[img]/images/graemlins/heart.gif[/img] ($0.46, 2 players)
Villain checks.
Hero bets $0.40
Villain calls

Turn: 9[img]/images/graemlins/heart.gif[/img] ($1.26, 2 players)
Villain bets $0.04
Hero calls

River: K[img]/images/graemlins/diamond.gif[/img] ($1.34, 2 players)
Villain bets $0.87 (all-in)
Hero hasn't got a clue what's going on.

I've been talking myself in circles. The fact he checked flop made me think he'd probably fold to another cbet, so when he called I thought Qx was likely. The tiny bet on the turn didn't make sense, but I thought that by calling at least I'd have a basically free card for a chance at making a pair. The river brought that along, but him going all-in only made me think KQ or some other lower 2 pair like K5 after all (I don't know why JT would stay around after the flop), which doesn't explain the turn bet but then I can't think what does. Now I still don't know what's going on. Should I raise the turn, call or fold the river? Should I be cbetting less/more or even at all? Maybe I'm thinking too much for 5nl. Thoughts?