AK pf, raise to get rid of limpers, shove on flop?

[mitodream]

PokerStars No-Limit Hold'em, 150k prize pool Tournament (Qualified through freeroll), 125/250 Blinds 30 Ante (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG+1 (t2432)
MP1 (t8703)
MP2 (t10725)
Hero (MP3) (t7980)
CO (t7277)
Button (t5100)
SB (t45)
BB (t8975)
UTG (t4613)

Hero's M: 12.37

Preflop: Hero is MP3 with A K
UTG calls t250, 1 fold, MP1 calls t250, MP2 calls t250, Hero bets t1000, CO calls t1000, 2 folds, BB calls t750, 2 folds, MP2 calls t750

Flop: (t4785) 7 , 2 , A (4 players, 1 all-in)
BB checks, MP2 bets t750, Hero ???

Should I have raised this much preflop, or more (shove)? What do I do on the flop? I have a pretty darn good stack. About 3700 left, and top 3000 get paid. Is it worth it to gamble knowing that these people like to call raises loose preflop (that's my read of this table)?

[fjuanl]

This is pretty much the best flop for AK without having 2pair+. With 7k left and almost 5k in the middle, you should feel very good about getting all your chips in.

Pre should be a little bigger...1250-1500 is fine. I wouldn't hate a shove either

[lNormajean]

1800/call pre, shuv flop. lots of worse aces in their ranges