You have $123 left on the flop. There is $16.50 in the pot so we should think about using Ribbo's rule of 13 here.
Divide the money you have left by 13, this is what you should be betting to get yourself roughly all in by the river. If the figure you get after dividing by 13 is smaller than the current pot, then you can bet a little bit less than the pot to build it. If the figure is larger, then you should be betting full pot each street as you will not get yourself all-in
So you can afford to bet $13 on the flop and $40 on the turn if you think you're ahead.
Now on to the important stuff. I think this is often a 4 bet preflop. Your 4 betting range needs to be wider than aces and this is a perfect spot for it. What is your opponents 3 betting range preflop? Is it more than 5% over a significant sample, if so then 4 betting is automatic.
A 4 bet would tell you a few things. If you get 5 bet, you can fold it, it's always aces. If he doesn't 4 bet, then you have to shove every ace high flop as he is seriously going to put you on AA and is probably calling with rundowns that he will toss on the flop or will be calling with a draw where your kings are good.
It also allows you to be all-in by the turn making your post flop decisions a lot easier in general.
As for how the action went down, most players with a draw will cbet this flop so I would go for the check raise. If villain checks behind the flop then i'm comfortable that at best he has a hand like AJ, I would expect strong spades to take a stab at this flop and check behind the turn.
If villain does take a stab, then I have to make a decision right here to fold or shove. I'm usually shoving barring a nitty read as firstly I still have 35% equity vs the nuts and secondly, I might find myself up against TT or 2 pair who has to bet the flop for protection.
Once this has happened the turn card is irrelevant since I have $65 left on the turn and the pot will be $150 so I have odds no matter what the turn is to stick the rest in. Sometimes I will need to hit my house, sometimes I wont.
As it is, the way you played it, you're obviously against a draw and it's a nice easy fold on the river. 
K 
K 
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