NL20 SH Speed JJ, A33 Flop OOP

IPoker, $0.10/$0.20 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $20 (100 bb)
BB: $25.77 (128.9 bb)
Hero (UTG): $20.10 (100.5 bb)
MP: $21.67 (108.4 bb)
CO: $21.43 (107.2 bb)
BTN: $25.62 (128.1 bb)

Preflop: Hero is UTG with J J
Hero raises to $0.60, 2 folds, BTN calls $0.60, 2 folds

Flop: ($1.50) 3 3 A (2 players)
Hero checks, BTN bets $1.05, Hero calls $1.05

Turn: ($3.60) K (2 players)
Hero checks, BTN bets $2.40, Hero folds

Preflop: Standard.

Flop: One of those ackward spots. I usually have the best hand, but if I bet and get called, it would by tricky to play the turn. This time I decided to check/call. Should we cbet and plan to cbet the turn if we will still be with 2nd pairs?

Turn: I usually check/fold the turn in this situation, especially when that card comes.

BTN: 21/17/0/67(3)/11/107 (VPIP/PFR/FtFlopCB/BetVsMissedFlopCB/AF/H)