Watching the replay. He raised minimum to 800. Had 6k+ left behind him. You had 16k+. Nothing wrong with the reraise imo. But when you raised it to more than 3k you put him at a position of calling over half his stack preflop out of position or reraising all in...which he did. He couldn't raise it in any form but all in.
So, if you are worried on calling his all in bet, the problem occurs with that larger 3bet. If you made it 2k only, maybe he fold or calls, or he raises all in regardless and now for 4k to call you question on calling that all in is more valid than how your hand played out, where you can only expect to call. You've got him covered, you're invested.
The way everything went down, I think this was good all the way. Player was around 16? BBs to start that was down to 14 after the minimum raise. I think your play would come with the caveat that you would call him allin had he reraised you, but had they folded because they were risking their tourney on an AQ os, out of position to a 3bet. Probably that player should have folded to your raise considering you had the amount of chips to eliminate them.
Looking back my numbers are off. I forget the already invested 800, so your raise was 2250 and player raised it 4k more. I'm still of calling here having a larger stack with the amount that would already be in the pot. But now seeing your raise was 2250 more, 5.5 blinds more I think you overbet the 3rd bet and it was enough to force his play. Raising 4 k was about the amount that could be cause for a bad call. Understanding their play in that situation. Didn't want you to call(wth are you calling my utg raise and 4bet?) can't you see I have strong hand? Them calling your 2250 raise would leave them on a loss on Shoving in until a double or triple up.
Just worked in your favor and that's poker.