Villain is 20/20 over 10 hands and is 4-tabling zoom.

So on boards like this, with an over pair, I like to either bet smallish for value from weak pairs/unpaired hands. Or I bet bigger, to get value from TPTK/weaker over pairs, since villain has a capped range. I'm not sure when to use which bet size, or if I should have other bet sizes on boards like this as well. Any advice would be appreciated.

[converted_hand][hand_history]Poker Stars, $0.02/$0.05 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $2.44 (48.8 bb)
BB: $5.01 (100.2 bb)
UTG: $5.26 (105.2 bb)
MP: $6.29 (125.8 bb)
CO: $5.33 (106.6 bb)
Hero (BTN): $5.71 (114.2 bb)

Preflop: Hero is BTN with Q Q
UTG raises to $0.20, 2 folds, Hero raises to $0.60, 2 folds, UTG calls $0.40

Flop: ($1.27) 9 2 6 (2 players)
UTG checks, Hero bets $0.46, UTG calls $0.46

Turn: ($2.19) 5 (2 players)
UTG checks, Hero bets $1.22

If you use a smaller sizing you can c-bet wider (value betting thinner by forcing wider floats and requiring less fold equity).

As long as you're using consistent sizing based on board texture then it's okay. There's nothing wrong with this on the face of it, and bet sizing is the most complicated part of hold'em. The 1/3 pot bet is something that's become increasingly popular.

Think about your range, and also consider what flops you want to play a 2 or 3 street game on i.e when you want to bet flop/jam turn and when you want to go small to jam river.

I think my 1/3 pot bet range is a lot more balanced, I can't really think of many hands aside from over pairs that I personally bet big with on this board. However I sort of hate seeing turn cards here... Am I giving too cheap of prices to continue with a 1/3 pot bet? Should I make all my bets 40% pot instead?

It's not like you expect him to have a ton of club draws when he raises UTG and flats a 3-bet. Your hand isn't very vulnerable at all to hands like TT/JJ though obviously we slightly prefer going large vs. those specifically before the board gets scary.