JJ sb, bad flop

[PokerDork]

The following hand came earlier tonight while playing in a decent 10/20 game. My image at this point is fairly tight and straightforward, and I've been hovering close to even all night. CO in this hand is somewhat loose aggressive preflop, but plays pretty sensibly postflop. Button is unknown but seems to be a solid TAG.
UTG limps, CO limps, Button raises, I 3-bet out of the sb with JJ. UTG folds, CO calls, button calls.
Flop: AQKr
I check, CO checks, button bets, we both call.
Turn 3r
Check, Check, Check
River 8
Check, Check, Bet I fold.
The buttons bet seemed weak here, and I really considered checkraising to drive out the CO who probably had me beat, but likely didn't have a hand he could call two cold with. The 8BB pot wasn't that big, so I folded. Two questions, should the flop be an auto-bet, and should I have check-raised the river?