2 table home tourney - QQ in BB

[Lunchbox420]

i think i found a tweak i should make in my live game, but i want ur guy's prospective...

we started with 10,000 in chips, blinds at 100/200 and go up every 20 minutes.

i had roughly 8000 in level 3, 200/400, and the cutoff raises to 1000, it folds to me, and i look down to QQ...

the raiser had plaid poker before, but was obviously very loose and didnt really know the game THAT well. so i raise it up to 4000 to go. he thinks for a few moments and reluctantly decides to call.

flop: 8s 4c 2c

i push, he calls, he shows 22, and my QQ dose not improve on a board of 872J8 and im out of the tourney.

now, onto what i think i need to tweak here.

would it have been a good idea to maybe check that flop, seeing how middle pairs make sets, and that board, with a loose/weak player, maybe play something like 44 or 22, with a raise of 3000 to him, and i thought with that call he had A4os-AKs, because with any middle pair he would have called instantly, instead of hesitating, from what i could tell.

but i also dont think i could have gotten away from this hand if i had to check call an all-in, but here would a check-fold be in order?