Poker Stars $15+$1 No Limit Hold'em Tournament - t25/t50 Blinds - 9 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

BTN: t1720 M = 22.93
Hero (SB): t1660 M = 22.13
BB: t1655 M = 22.07
UTG: t2015 M = 26.87
UTG+1: t1370 M = 18.27
UTG+2: t1210 M = 16.13
MP1: t1230 M = 16.40
MP2: t1205 M = 16.07
CO: t1435 M = 19.13

Pre Flop: (t75) Hero is SB with K K
2 folds, UTG+2 raises to t150, 4 folds, Hero raises to t450, 1 fold, UTG+2 calls t300

Flop: (t950) A 3 J (2 players)
Hero bets t760, UTG+2 calls t760 all in

Turn: (t2470) 2 (2 players - 1 is all in)

River: (t2470) 4 (2 players - 1 is all in)

Check/fold flop or shove?

With less than a pot sized bet we can't get away from the hand. I like c/c here to give him a chance to do something stupid like shove 55 (believe me they do), or maybe bet something really weak like 200 to give him some illusion of FE.

I like shove pre. Hes calling anyway.

This.
As played c/c.

well check-calling would make sense because its not that likely that they are capable to call you with worse given the preflop action and the flop bet. I would put you on AQ, AK, maybe KK... And a villian who is calling with an A preflop is never folding on this flop.
A check might induce a bluff or a bet with some weaker hands like KJ, QJ, 66-TT...

If he has the A it shouldnt bother you that much because hes preflop action was just terrible. I dont like pushing preflop because it might allow him to make a correct lay down and im not sure if we want to reach this target.

I d prefer the same raise and to bet most of the flop without an A and strife for a check-call on a board like this.
Generally a check could also be right on a none A board if the only way to get more money in the pot would be to induce a bluff by checking. If he improved his hand to top pair or hes holding an overpair the outcome would be the same if you are betting or if you are checking. A player whos calling a bet with a hand like in this specific situation is also very likely to bet in this situation so it doesnt matter i guess.

actually i like check calling here for sure. People turn pocket pairs into bluffs more often than you think.

Shoving pre is probably better, but 3-bet is fine against some villains. You are never folding out A-x by shoving the flop, so check-call it and give him a chance to bluff with worse hands.