Preflop
Pretty standard by both players, and the main thing, I would point out, is, that your 4-bet was very small. For this sizing and in position he is getting the odds to call with pretty much anything, that was good enough to 3-bet, and certainly with AQs. Folding AQs getting almost 3:1 and position would be insanely nitty and even more so in a late position battle like this.
Flop
In a 4-bet pot I would generally tend to bet a little smaller to give him a tough decision with all the hands, that missed. If he has exactly JJ or QQ, you are getting his stack on most runouts anyway, but he could also have a lot of hands like A high, that missed, and have an easy fold, when you bomb it like this. For him he has a standard call with the nut flushdraw and two overs.
Turn
As played you only had a pot sized bet left, so anything other than jamming would be fairly awkward. Villain was only getting 2:1, so he needed around 35% equity factoring in the rake, and even a 12 out draw, assuming his A was life, only has 25%. He did beat a bluff though, and for that reason its probably an ok call. If your range was JJ+, AKs (for partial AK) and A5s (as a representation of bluffs), then he had 36% equity.
Now at 5NL it can be argued, that the general population dont have bluffs, when they take your line, so folding could be a reasonable adjustment. But if you move up to 25NL or higher, you need to play AQs exactly like, your opponent did, because otherwise people can just bluff you to high heaven.