$10 NLHE 6-max: Folding second pair with such great odds

A few hands prior to this I had taken a chunky pot from BTN so I was prepared to call the small raise from him on the river in case he was just having a go. However when the calling station comes along we can never be good right?

Also, do you ever bet flop or turn here? And do you bet river for value as I did?

poker stars, $0.05/$0.10 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

SB: $10 (100 bb) 36/0/0 60 Hands
Hero (BB): $27.47 (274.7 bb)
UTG: $14.30 (143 bb)
MP: $10 (100 bb)
CO: $4.69 (46.9 bb)
BTN: $36.72 (367.2 bb) 36/21/8 120 Hands

Preflop: Hero is BB with Q Q
3 folds, BTN raises to $0.30, SB calls $0.25, Hero raises to $1.20, BTN calls $0.90, SB calls $0.90

Flop: ($3.60) J K 5 (3 players)
SB checks, Hero checks, BTN checks

Turn: ($3.60) 3 (3 players)
SB checks, Hero checks, BTN checks

River: ($3.60) 4 (3 players)
SB checks, Hero bets $1.99, BTN raises to $4.50, SB calls $4.50, Hero???

Draw heavy board, I probably just cbet flop but I don't mind checking. I am almost always betting this turn and I really see no need to bet river.

Bet the flop, bet the turn... I think normally you could fold the river, but maybe against this opponent I'd call at your stakes. He seems to be likely a bad lag... no hands really makes sense for him unless he has 44 or decided not to be the turn w/ 67.