Warning: What I'm about to say may sound crazy.

I wouldve checked the flop in this situation. First off whenever I 3 bet preflop in your situation I will bet the flop around 99% of the time. But there are times I will check even after I 3 bet preflop, and now I will explain to you those times.

Whenever I am against a super lag and i have a strong showdown hand like AQ and I 3 bet OOP like in the SB like in your case and the flop comes out xxx such as your case, I like to check and call all the way, this line may seem preverse, but against super lags, playing this meekly and letting them bluff their chips off can work very well. Here are the benefits to this strategy.

First off against true maniacs who will bet every time you check, you should be checking and calling alot with your marginal hands. This includes any pair type hands or Ace highs. By playing this way, you will minimize your loss when you have the worst hand, and when you have the best hand you will never miss out on any bets since the maniac will bet for you, and most importantly by takin this line you will never get outplayed. So when you 3 bet with AQ and the broad came out K84, consider checking and calling all the way, cuz IMO your hand is too strong to consider folding postflop even on this board against this super lag, and I promise you he will bet many worse hands than you all the way. Understand that on a K84 board you are still a favorite to have the best hand against this superlag, and by betting the flop you only encourage him to fold hopeless hands, or raise you with better hands or bluff raise you. So betting the flop actually costs you money since you miss out on all that money you could make if you checked and called and induced him to bluff all the way, and you make the hand harder to play since if he raises, you will be left guessing whether this time he has you beat or is he raising on air.

So my contention is against super lag maniacs when you raise with a hand OOP with showdown value like AQ and you miss the flop, consider checking and calling all the way. You should also play this way even if you hit the flop like if you had AQ and it came out A84, you should again consider checking and calling all the way and maybe checkraising the river. By playin this way against a maniac you will effectively take away all their power, since by checking and callin they can never push you off the best hand. When you acutally hit a good hand like top pair, many times you will induce the maniac to bluff all the way with no outs which is wonderful for your bankroll. and when you have something like Ahigh, you will induce him to bluff all the way with 6 outs which is still a good situation for you, and even if he hits the turn or river, dont worry about it, thats just poker.

Against these type of players, getting to the showdown with any hand that has some value is exetremely important IMO. check and call with your marginal hands and your strong hands to balance your strategy and I promise you, you will take all their money in the long run.