You want to be 4 betting Qs for value when you get squeezed close to 100% of the time - unless you know the guy squeezing is an absolute nit that can only have AA KK AK.

As played bet the turn bigger for value, at least 2/3 pot. Once beekeeper calls you want to be jamming river to get value from his 1 pair type hands. If you check he will check back all his Tx 9x and under pairs to the 9 which is obviously terrible for us.

Getting value here far outweighs the chances of villain having a draw that missed and him jamming the river when checked to.

Makes a lot of sense and clearer for me thanks, if I 4 bet QQ what is the best sizing and if he shoves I assume I fold as I never really see anyone at these stakes Gii with worse, except short stackers of course.

If we 4b QQ for value were basically never folding pre flop at these stack depths.
We 4b for value because villain can have some bluffs in position and we don't want to play a multiway pot OOP + give Beekeper the price to see a flop with likely a weaker hand than ours that can flop a set 2 pair or huge draw that will have us in trouble.
We want to 4b to around $7 - simply put I usually double the raisers raise size and add 4 or 5 big blinds when out of position facing a squeeze because of the dead money in the pot.
Once we've done this and villain jams he's never bluffing and were not loving life were hoping to see AK which would be enough to make this call totally fine.

Long winded but felt the explanation would be of benefit

Pre: I don't hate calling here but 4betting it would be my preference. The issues we have with flat calling is that it encourages an extra caller in behind us and we put ourselves in a spot with a reasonably vulnerable hand that will be tricky to get away from on a lot of boards where we could be beat. I would typically be going a little larger than @Curl-1-out suggested but only by a small amount, I would normally go around 7.50-8 here but I don't think it's going to make a huge difference either way to the overall outcome of the hand.

Flop: As played, I quite like checking here to continue underrepping our hand and to encourage a c-bet here.

Turn: I feel we should be going larger here for value. The chances of our hand not being best now are extremely slim and we want to maximise our value, I cannot think of many hands that will call $4 that will not call $6. By going on the smaller side we are just missing out on too much value here.

River: We should definitely be betting here again. As beekeeper has left that pot behind the only move I see here is to jam. The chances of us being beat here are almost non-existent the way the hand has gone, the only thing we accomplish by checking is trying to get him to bluff a hand like QJ, the times we get value from all of his showdown value hands that would not be betting when checked to outweigh this possibility though.

Opening UTG and getting squeezed vs an unknown I don't mind the call pre at all. If he's never stacking off with worse than QQ+ AK you're not going to be doing well. Even though it's not great playing OOP here it will still be a +EV spot.

I would make the turn size bigger due to the pre flop raiser not looking interested and the other guy being a short stack making it likely he's bad and calling a wide range including many Tx which can pay you over two streets.

On the river I would just go for a shove. We're now beating T9 and there's more Tx in his range than whiffed QJ to get value from. It's really not worth trying to induce here.

Hi all, I'm a little confused here.

If we're up against an 'unknown' how do we know they'll only ever stack off AK/QQ+ preflop anyway? I think the play is 4bet and go with it without info.
It's surely standard stuff preflop? Player A raises from early, player B flats their pretty whatever, player C squeezes with the boss position and takes it down; I do it all day.

Would appreciate any explanation please.

As it was played I would bet enough on the turn to get the money in on the river and just ship it on that board.