Villian is 40/11.5 over only 52 hands

Is bet/fold a better play here on the flop than check/call and if a third spade did land on the turn do I continue anyway given he could be playing any Ax, AJ is a possibility, Jx or air here since I showed weakness to the A on the flop.

Full Tilt No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

MP3 ($46.85)
CO ($19.95)
Button ($91)
Hero ($74.90)
BB ($52)
UTG ($68.35)
UTG+1 ($52.60)
MP1 ($88.35)
MP2 ($57.35)

Preflop: Hero is SB with K, K.
2 folds, MP1 raises to $1.75, 4 folds, Hero raises to $6.25, 1 fold, MP1 calls $4.25.

Flop: ($12.75) J, A, 5 (2 players)
Hero checks, MP1 bets $5, Hero calls $5.

Turn: ($22.75) 7 (2 players)
Hero checks, MP1 bets $10, Hero folds.

Final Pot: $32.75