This can be a fairly easy decision with a little insight. First - everything hinges on your villain's 3 bet range.
At lower stakes in particular people tend to 3 bet cards like 44-TT, in addition to JJ-AA. They also 3 bet AJ-AK. This is because they aren't comfortable playing post flop with hands like AJ and would rather see a fold before the cards are laid out. There's a good portion of this range that QQ crushes. Even if the player who raised first is on the tighter side, you can leverage the 4 bet here because the initial raiser will have to consider the villain shoving behind him. Two folds for the price of one. Unless the villain does shove, in which case, you have to make a decision...
The table matters a lot too. If the table is tight, 3 betting with position is often a sign that the hole cards are NOT AA/KK. People with hands this strong generally want people in, not scare people out. So look out for flats to a big early raise, or min-raise 3 betting. On a loose table with hitch hikers, people are more likely to 3 bet in position to shake off the tag alongs (or catch a loose caller for value).
Then you've got people who are 3 betting tight. JJ-AA, AK/AQsuited. You have value against this range. So you're basically set mining with a touch extra
equity. So you're basically looking for info unless you happen to hit your set.
If the player calls - you either have A) A calling station, or (B) someone with a preme hand. If you hit your set on the flop you can effectively check to either person. (A) will make a bet with about half their range, (B) will make a bet with pretty much all of their range. (A) you can sometimes check-shove and get a call from AA/KK, or even AQ. If they don't have that stuff, a check-call will shut them down anyway. So I like the check-raise for scenario (A). (B) I like a check-call. They're looking for information, check-raising gives it to them. However, a check-call looks like you hit the Queen (puts your perceived range to AA, KK, AQ,KQ, QQ, QJ suited on the loose side). AA and KK are beating a lot of that range! You'll probably see more value down the line. JJ, AK will probably shut down, AQ will fold under pressure. TT, you'll likely see a lot of value!
I like leading out on the turn. It looks less strong than flatting to a 3bet, check-calling the flop, check-calling the turn. To me, that signals AA, KK, or QQ in your hand. By leading out I feel that's a stronger indicator that you have AQ or KQ. If someone with Aces feels you paired your Queen they might look to get value.
Another prospect on the turn I actually like the min-raise donk lead. It is a bit of a flag for a more experienced player, but it can also look like a protection bet. A more experienced player will often raise here to see if you are protecting or if you have a made hand. Experienced players are looking for a show down with AA/KK if they think something sneaky is happening, so this is your last point of value for a good player generally. A less experienced player will usually elect a call, which means you should be able to lead for value on the river (a little more than half pot is usually about right) and get called. It's hard to let go of top pair to a value bet on the river even for an experienced player, even if there's that nagging feeling that they're beat...
The most value is always going to come from the loose-aggs though. They live for AA. They design their image around getting all their chips in with Aces. At least at the lower stakes. All you have to do is show them the slightest sign of weakness or hesitance and they will be rushing into the pot faster than you can figure how to get value. This ideal though, you'll generally run into this if you have something like 55 pre-flop where you're putting them on AA/KK and flatting for a set.
