KK turn move?

Figured i'd post my first hand. It's very simple but want to ensure i'm thinking along the right lines.
Villain is 22/15/4 250 hands.

PokerStars No-Limit Hold'em, $0.10 BB (9 handed) - PokerStars Converter Tool from FlopTurnRiver.com

UTG+1 ($10)
Hero (MP1) ($27.74)
MP2 ($13.38)
MP3 ($14.36)
CO ($4)
Button ($8.17)
SB ($13.16)
BB ($3.99)
UTG ($1.95)

Preflop: Hero is MP1 with K, K
2 folds, Hero bets $0.30, 4 folds, SB calls $0.25, 1 fold

Flop: ($0.70) 3, Q, 3 (2 players)
SB checks, Hero bets $0.40, SB raises to $1.20, Hero calls $0.80

Turn: ($3.10) Q (2 players)
SB checks, Hero ???


I've seen him 3bet QQ and AK preflop. When he raises the flop i'm thinking AQ,AXs or an underpair and attempting to get me to fold.
Is checking behind the best option on the turn?

Strange line. Looks more like a failed bluff to me. Queen or not though, there's no value to betting here except for the rare time he has AA and folds to a turn bet.

sounds good

agreed on the above. check and maybe u can get fancy and bet something small on the river to induce a bluff or get some light calls

Check turn behind intending to call most river bets.

Easy game.