9 max SnG 0.5$ hand AK fd oop

I consider several possible sequences of action here
First is to check/call the flop if we have good pot odds for playing the turn or if we are given bad pot odds, we can reshove directly. The big disadvantage of this is that we will often look like a fd and we not be given implied odds on the next streets.
If he checks behind we can bet the blank turn trying to put him out and steak the bank. If he raises we are good to fold.

Second option is to bet myself and respresent a made hand that is afraid of fd. 1/2 the pot would be enough. If we see a c/r we shove and if we see a call we don't bet the turn and we evaluate a call EV. Should the latter be lower that our call equity we fold.

I would definitely bet this flop. If we are behind we very likely have 6 outs from overcards as well as the flush draw outs. If villain also has a flush draw, we want the money in the pot so we can take his stack on later streets. It keeps us balanced for when we don't have such a good hand in this spot (may not matter versus this villain at these stakes, but worth noting). Finally we have fold equity, and there is nothing wrong with taking down the pot right away.

RedHeater, what about the turn. What is the best way to play it?
As for the balancing. Can you elaborate and give an example of a weaker hand and reason why we would do the same? It would help me a lot. Thx in advance! Cheers!

Flop: I would bet around 70% of the pot to scare him off.
Turn: I would barrel the turn because he seems very passive. The plan is to get many chips in the middle to get value in case we hit one of our many outs but not commit to the pot. Stacks are deep enough to achieve that through the river.