Villain has been a bit bluffy 38/20/3.4/112. Hero has been TAG

PokerStars No-Limit Hold'em, $0.05 BB (5 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

BB ($7.06)
UTG ($6.03)
Hero ($15.22)
Button ($14.36)
SB ($13.56)

Preflop: Hero is MP with K, K.
1 fold, Hero raises to $0.2, Button calls $0.20, 2 folds.

Flop: ($0.47) 5, K, 3 (2 players)
Hero bets $0.3, Button raises to $0.6, Hero calls $0.30.

Turn: ($1.67) 5 (2 players)
Hero checks, Button bets $1, Hero raises to $3.25, Button folds.

Final Pot: $3.67

Standard or did I lose value from c/raising the turn?

I think so. I know that when you see a guy with stats of 38/20/3.4 at these stakes, it usually means that they'll flat you PF with really really wide range.

That being said, I think his range on the turn is composed mostly of air based on the stats.

We really need to know his range to figure out how to get the most value.

You said the villain is a bit bluffy so some % of his range is going to be total air. I think a lot of mid pair type hands are in his range also due to the flat call on the button preflop. It is unlikely, but still possible, that he has a King since 3 of them are already out. He could also have 5X sometimes and straight draws.

I think his range would be something like: Midpairs (50%), Air(30%), 5x (10%), Kx(5%), Straight Draw (5%)
Does this seem reasonable?

That's the type of range I would be putting him on given the description.
It's clear that most of those hands cannot stand a check-raise on the turn and you will fold out a lot.

i really like the bet/raise/flat call on the flop
but if you know he's bluffy, en you check/call on the turn, will he bluff still on the river?
if the answer is yes, check/call the turn and check/raise the river
if the answer is no, you can either go for check/call and then bet
or the check/raise
but i liked the way you played