Should Hero have called villain's pre-flop raise, re-raised, or folded?
The only thing you can do is call. You've labelled Villian as tight-aggressive and he's made a small reraise after you've opened under the gun. This is a fairly strong sign of strength. Let's look at your options:
Jamming: KQs is doing badly against the average TAG players range in this spot. Even if you give him a generous range of {99+, AJs+, AQo+, KQs}, KQs has 32.42% equity against this range. He isn't folding enough of that range to a jam to justify doing so.
Reraising Not-All-In: This is a bad idea. The majority of his range will jam if you reraise at which point you'll have to fold, giving up a significant pot. The rest of his range will likely call and go to a flop. Note that his calling portion isn't doing so bad against KQs either.
Calling: You flat his raise and go to a flop. The total pot is $58 and you only need to call another $15, giving you 3.87:1 odds; a very tempting proposition. Note that you'll have to play this hand out of position against a very strong range. You are giving excellent reverse implied odds in this situation. If your postflop skills are good you should be fine though.
Folding: This is definitely an option. It really depends on just how tight Villian is. If he's extremely tight I would fold this without a second thought.
So, the process of elimination only truly leaves you two options: call or fold. If you are fairly confident he's not a nit, see a flop.
Let's pretend Hero knew the villain had QQ on the flop. How much would Hero need to bet for villain to fold?
I'm sensing a flawed thought process here. You do not want Villian to fold QQ on the flop. You should be betting for value, not as an attempt to fold out his hand. You don't want to fold out the portion of his range you're beating. You want to extract chips from him.
I would personally never be betting this flop. You're out of position against an opponent that 3-bet your UTG open preflop and you've flopped TPGK which is still very vulnerable against Villian's range. He either has you crushed right now or has a hand that is scared due to the King.
Take a step back and think what leading out accomplishes. You simply fold out {AQ, AJs, QQ-99} a certain amount of the time (how often is dependent on how tight he is) and you valuetown yourself against {KK+, AK}. It's unlikely that Villian will fold to any flop bet with QQ, apart from a jam, and especially not against a $30 bet into a $73 pot. That means you will have to barrel the turn to push him off his hand which I just can't see happening with such short stacks. And that would be a terrible line to take as his range is very strong. You might as well just hand him your stack.
Consider checking. This way Villian will likely continuation bet his entire range, {KK+, AK} as well as the hands you're beating, {AQ, AJs, QQ-99}. And if he doesn't, you can be reasonably confident that he doesn't have {KK+, AK} and then you can bet the turn/river for value against {QQ-99}.
Your hand is relatively weak when compared to your opponents range but it is too strong to entirely give up on though. When you are in this kind of position, you should think of your hand as a bluffcatcher.
To answer your question entirely, if I for some reason decided to lead the flop here I would still bet $30 as you did, but for a completely different reason: for value. $30 bet into a $74 pot on the flop and then jam the remaining effective $85 on the turn when the pot is $134. If I was going to try to push him off {QQ-99} I would just jam the flop (but I can think of literally no situation I would ever do that).
OP EDIT: If you were the villain with QQ on the flop, how much would hero have to bet to get you to fold?
~$50+ when facing a tight-aggressive player that raised UTG, smooth called a small reraise, and then donk-bet 2/3rds pot on a super dry K52 rainbow flop. Tight-aggressive players just aren't doing this with worse than Kx. If he had {QQ-99}, he'd likely just check-call one or two streets. He also might be donk-betting with Ax hands that missed but it's such a small portion of his range you can usually ignore it, especially when you consider that most people won't continuation bet 2/3rds pot with air. They'll c-bet around half pot or slightly less.
If he donk-bet less, say $30-$40, I'd call one street and reevaluate on the turn. In this scenario, once I've hit my set I'm getting it in. Any non-Queen turn I would give up if he continued betting and if he didn't I'd check behind. Same on the river.
This changes drastically if you can't label your opponent as tight-aggressive. If he is even remotely loose, I'd be getting it in with QQ on K52 rainbow every time, every day. I'd never be folding.