How many players were on the table? If it was short-handed then UTG+2 means something very different to if it was 9 or 10 handed.
3betting is much more interesting in the first instance than in the second instance. 3betting AQo vs an early position raise is generally pretty bad. Especially when fairly deep and out of position, and especially when your opponent is competent. You should depolarise against poor players who will play weakly postflop, but out of position to a good player it is much better to show him respect and flat AQo when he has raised from EP.
You might think "Yeah but I am going to miss the flop more often than I hit ... isn't it better to 3bet so I can take the initiative and hope to win the pot even when I don't hit the flop?" This works okay against bad players who are going to call your 3bet with most of their range, and then just meekly fold to your cbet when they miss the flop. But a competent player will not just give up on every flop he misses. He will continue on many flops even when he misses, by either bluff-raising or floating with backdoor equity hands.
It might feel 'weak' to call the raise then check-fold when you miss the flop. But it is going to feel even weaker to 3bet pre, then cbet the flop, then check fold the turn. You hand may feel 'hard to play' without the initiative and out of position. But believe me, it is going to feel MUCH MUCH harder to play in a bloated 3bet pot with deepish stacks if you cbet the flop and your opponent does not fold!
This is even sometimes going to be the case if you flop top pair. Imagine you 3bet pre and the flop comes something like
. You cbet your TPTK and villain calls. How happy are you feeling now? It's not like the SPR is really low now so you can just get all-in comfortably on the turn. If your opponent was a bad player you'd probably be feeling okay about things. But against a good player what are you doing on most turns? Is your opponent really going to stack off with something like KQ or AJ? He is a good player, not a spew monkey.
The trick is to realise that when you just call preflop you don't have to check-fold every flop that you miss. You can make a few check-raise bluffs, and you can float some flops out of position. Sometimes you get Ace high to showdown and win. Sometimes you pick up a second barrel when an Ace or Queen turn. Other times you can bluff the river.
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