AK makes top pair on turn & gets check-raised from BB (5NL micros)

I have AK in LP w/ a big stack and since it's the 5NL micros, two people open limp (of course) so I put in a nice hefty 5bb +1/limper raise. The BB, who is very loose & fairly passive, calls. Unwisely perhaps, I bet the flop hoping to make him fold (ok, I know, fish don't fold, and that one third sized bet wouldn't do it anyway -- I know, that was mistake number one). But happily I make my TP on the turn ... and then I get check-raised.

Full Tilt - $0.05 NL - Holdem - 9 players
Hand converted by PokerTracker 3

MP: $6.56
MP+1: $5.29
LP: $12.64
Hero (CO): $9.53
BTN: $5.00
SB: $1.64
BB: $5.66
UTG: $15.19
UTG+1: $5.17

SB posts SB $0.02, BB posts BB $0.05

Pre Flop: (pot: $0.07) Hero has A K
fold, fold, MP calls $0.05, fold, LP calls $0.05, Hero raises to $0.35, fold, fold, BB calls $0.30, fold, fold

Flop: ($0.82, 2 players) 2 J 4
BB checks, Hero bets $0.30, BB calls $0.30

Turn: ($1.42, 2 players) K
BB checks, Hero bets $0.80, BB raises to $2.00,
Hero....?

*Folds, and give the fish credit?

*Calls, hoping he made his TP as well but had a weaker kicker (like KQ), or maybe we'd split the pot if he had AK? Btw, even w/ a KXs diamond flush draw I'm 73% to win.

*Shove?