Go ahead and re-raise this flop?

Preflop: I would raise. I don't think "slowplaying" AK preflop is generally a good play.

Flop: I would 3-bet. There are 13 SB in pot when it comes to you, and your 3 opponents will likely call one more bet. It may reduce the number of bets you can get on the turn, but it is now going to be a big pot that you should focus on winning by thinning potential FH draws.

Turn: Having called on the flop, I like the check-raise.

River: Good.