I'm new here - although I've read the board on and off for about ten years - and my sense is that most commenters are better players than I am, as I've never played $20/$40 (though I've played a ton of $1/$2 and some $3/$6 online over the years), so there's my disclaimer.

Why not raise QQ pre-flop? It's not "sort of" a premium hand; it's a top 5 hand.

I understand your range is wider if you just call PF, but if the button is a lag and is opening from button, his range is basically anything he'll play, so your three-bet would not limit your range as much as other 3-bets would in other positions. You could have any pair, any two face cards, some stronger suited connectors, etc. I get 3-bet all the time by hands like 22-44 in situations like these, where I open on the button.

Then bet the flop. I see a lot of lags raise the guy who leads the flop almost regardless of holdings, so consider re-raising if raised.

From my experience, a flop check-raise likely limits your range to exactly what you have - second pair. So even if you're ahead, I think your cards are face-up at that point. If I were the lag, I would put you on 2nd pair... Maybe a draw.

Betting the flop after 3-Bet pre would also prevent you from wondering, for example, if he hit the str8 on the river - he totally could have cbet 87 (suited or not) on the flop, but I doubt he would call a bet with that hand, unless it were suited with clubs.

If you're wondering where to place the aggression, I'm going with PF. Max your premium hands!

It's like Mickey said in Rocky II after Adrian wakes up and gives Rocky the go ahead to fight Apollo: "Well what are we waiting for?!"

There’s nothing wrong with three betting pre here. I’ve adopted a strategy of. Never three betting pre out of the big blind in a heads up situation to keep my range wide and potentially make more $$$$ post. I’d three bet this multi way or from any other position.

Not having a 3 betting range is fishcake central unless it's an exploit against this specific opponent.

So you're getting bets into the pot when you want your opponent to fold, but you're not getting bets into the pot when you want to be called? I'm not sure where you're getting value postflop to make up for the lost value preflop.

This also seems like an incredibly transparent strategy. There are a lot of paired boards and your logic holds fairly consistently in all of those situations.

flop seems like an easy CR vs. described dynamic, but id 3 bet preflop so he can 4 bet and then i cr the flop.