2nd hand at table so no reads.

Preflop is standard, when he checks it to me I cbet to take it down right there. I'm not sure if I should have 2 barreled the turn once the board paired, at 2NL at not sure its that profitable.

The river is at least a call getting over 5 to 1, should I shove here?

PokerStars No-Limit Hold'em, $0.02 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

MP ($6.06)
CO ($5.09)
Hero (Button) ($1.97)
SB ($2.26)
BB ($7.25)
UTG ($2.71)

Preflop: Hero is Button with J, A
UTG calls $0.02, 2 folds, Hero bets $0.10, 2 folds, UTG calls $0.08

Flop: ($0.23) Q, 9, 10 (2 players)
UTG checks, Hero bets $0.18, UTG calls $0.18

Turn: ($0.59) 10 (2 players)
UTG checks, Hero checks

River: ($0.59) 8 (2 players)
UTG checks, Hero bets $0.25, UTG raises to $0.50, Hero raises to $1.69 (All-In), UTG calls $1.19

Total pot: $3.97 | Rake: $0.15