The flop was so dry that I thought a raise would draw him away for sure. If he had QQ-AA he'd probably keep firing anyways, and if he had AK/AQ i wanted him to either catch a pair or try to bluff again. Is there any particular reason why I shouldn't have slowplayed the flop?

Should I have shoved the turn? Or was shoving any river still okay?

PokerStars No-Limit Hold'em, $0.02 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG+1 ($4.95)
MP1 ($1.91)
MP2 ($4.73)
MP3 ($5.11)
CO ($2.84)
Button ($1)
SB ($4.88)
Hero (BB) ($2.04)
UTG ($2.94)

Preflop: Hero is BB with 6, 7
UTG calls $0.02, 3 folds, MP3 raises to $0.12, 2 folds, SB calls $0.11, Hero calls $0.10, 1 fold

Flop: ($0.38) 7, 3, 7 (3 players)
SB checks, Hero checks, MP3 bets $0.35, 1 fold, Hero calls $0.35

Turn: ($1.08) 4 (2 players)
Hero checks, MP3 bets $0.36, Hero calls $0.36

River: ($1.80) 8 (2 players)
Hero bets $1.21 (All-In), MP3 calls $1.21

Total pot: $4.22 | Rake: $0.20