I don't feel I extracted as much as I should out of this hand. I checked the flop hoping/expecting to see a cbet from either the CO or Button, did I bet too hard on the river?

PokerStars No-Limit Hold'em, $0.25 BB (5 handed) from (Format: FlopTurnRiver)

BB ($29.05)
UTG ($8.25)
MP ($33.45)
Button ($25)
Hero ($24.75)

Preflop: Hero is SB with 4, 4.
1 fold, MP raises to $0.75, Button calls $0.75, Hero calls $0.65, 1 fold.

Flop: ($2.50) 4, 2, Q (3 players)
Hero checks, MP checks, Button bets $1.5, Hero calls $1.50, MP folds.

Turn: ($5.50) A (2 players)
Hero bets $3, Button calls $3.

River: ($11.50) 7 (2 players)
Hero bets $8, Button folds.

Final Pot: $19.50

Results in white below:
Hero has 4c 4s (three of a kind, fours).
Outcome: Hero wins $19.50.

Your set is hidden - Lead out on the flop and hope to get re-raised. With that board you could slowplay (call) a raise to the turn as only a small str8 could be drawing to it but with a more connected board you might just go for the re-re-r right on the flop.

The ace on the turn was a real action killer - you really have to go for a check-raise here. Leading out looks like you called with A-weak kicker preflop and on the flop so are very likely to have 2 pair and a draw to a bicycle str8. Checking keeps up the appearance of weakness and Btn has another chance to protect his hand or fire a second shot at his bluff.

A CR on the turn is usually a bigger sign of stregnth then a CR on the flop. Either way you need to find a way to get money into the pot so that you have a chance to stack him. There are 3 ways to do this. Lead the flop and hope he reaise. CR the flop, or CR the turn. I like the first 2 options better than the third. The ace can be a bit of an action killer unless the villian happens to have an ace.