Villain had just taken down a few pots. Haven't saw anything until now

PokerStars No-Limit Hold'em Tourney, Big Blind is t30 (8 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP1 (t1445)
MP2 (t1855)
CO (t3170)
Button (t2265)
SB (t2294)
Hero (t1440)
UTG (t480)
UTG+1 (t551)

Preflop: Hero is BB with Q, A.
UTG calls t30, 3 folds, CO calls t30, Button calls t30, SB completes, Hero raises to t120, UTG folds, CO raises to t210, Button folds, SB calls t180, Hero calls t90.
Flop: (t690) 7, 3, 8 (3 players)
SB checks, Hero checks, CO bets t420, SB folds, Hero?

Main question is if I should have shoved PF. Suggestions?

Shove over a reraiser PF with AQ at blinds of 15/30? No way. Call the reraise and reevaluate on the flop. Let it go when you miss. AQ is a potential trouble hand in the early stages of an STT (which I'm assuming this is).

Wow this is an extremely lose table. So two limpers a raise, a mini raise, two calls. I am completely letting this go. The mini raise is screaming monster and there will be better spots. Like Jmbreslin says, AQ is a great starting hand - but like AK it is a drawing hand and you need to get rid of it when it misses.

If it wasn't for that mini raise - say everyone flat called - then I would cbet into this flop preparing to lay it down if raised and check/fold the turn if called.

make the raise larger. w 4 limpers, make it 180 or something. The CO rr and that's just a strange move. But, a bunch of callers so nothing wrong to call. However, if you don't hit the flop big time, you have to let it go instantly. I'd only put more money in if I hit trips, straight or something like 2s, Qs, 7s etc...

I think hes talking about pushing as his first action, not in response to the reraise. Its a gamble at that point because you are probably getting called by a small to mid-pair that thinks youre just squeezing, so youre racing from behind without that much dead money. I doubt theres any big hands out there.

As played, insta fold. Thats a flop that can hit too many hands that can limp/call.

Still, my answer is the same: no way. Far too early to be shoving over limpers w/ AQ. If this is micro stakes I might actually be inclined just to check in the BB rather than raise to begin with. With 4 limpers you'll have to make a big raise to thin the field, and even then you'll likely end up bloating the pot and having to make a big CB when you whiff (or check-folding against several villains). Good way to bleed chips early.

limpers play mid connectors (s or o) and sm-mid pp. the CO re-r smells like a pp. That flop looks like a limper's dream flop with 2 likable sets (7s & 8s) and a 3rd not as likable (3s), along with a flush and str8 draw. It all adds up to MUCK the over cards - you need runner-runner to even get into contention.

As for the preflop push - too early and the blinds are small enough to look for a better spot

I either raise to ~180-240... or I simply check the bb. Odds are, you're going to get a few callers, and you're not going to invest anything more if you miss the flop.

Hands like A10-AQos don't play well post-flop in multi-way pots out of position... I think I raise here to 200~ 35-40% of the time, and just check most of the time. Maybe that's nitty, but in micro-donkaments it's all about getting position on your opponent or having made hands out of position... imo.