This is a rare example of me feeling I should stray from MSS rules. The button is unlikely to have more than 2 outs on the flop, so playing rope-a-dope seems right to me. He is quite likely to have a pair due to the preflop action, but should be less inclined to put in more money if raised on the flop. On the turn, I know the button has no outs, so it's about maximising the pot size. If the button has a small to medium pair (or less), a raise here might be counterproductive. On the river, I feel a bet is likely to be called rather than raised, but check-raises often get called by players who have led all the way (I must stop making that mistake myself). Interesting how I got a more tilty response than the call I was hoping for. I suppose he assumed I had a jack and felt he could bluff me off it. Not a difficult final call. 
Hand converted with online PokerStrategy.com hand converter:
$0.02/$0.04 No-Limit Hold'em (9 handed)
Known players:
[tg]CO$5.78:///////;BU$5.47:///////;SB$1.45:///////;BB (Hero)$1.72:///////;UTG1$6.89:///////;UTG2$4.47:///////;MP1$4.00:///////;MP2$2.98:///////;MP3$4.82:///////;[/tg]
Preflop: Hero is BB with 6:c, 3:h.
UTG1 folds, UTG2 calls $0.04, 4 folds, BU calls $0.04, SB calls $0.02, Hero checks.
Flop: ($0.16) 3:c, 3:d, 2:h (4 players)
SB checks, Hero checks, UTG2 checks, BU bets $0.04, SB folds, Hero calls $0.04, UTG2 folds.
Turn: ($0.24) 3:s (2 players)
Hero checks, BU bets $0.24, Hero calls $0.24.
River: ($0.72) J:d (2 players)
Hero checks, BU bets $0.15, Hero raises to $0.80, BU raises to $1.45, Hero calls $0.60.
Final Pot: $3.57.
