The villain with the big stack was playing loose, and not too aggressive.I think the best line here is a check, but I don't like to give a free card to a flush draw.
He called pre-flop and on the flop, there are many hands that fit his action and beat you are KQ/KQs, QJs, QTs, 22, 77. I would check here. If the villain isn't aggressive as you say, then he won't probably try to steal the pot so check-folding seems a good option.
I like the check-fold line.
Bet. He has a very big stack and he is a loose player, so he can be playing many hands here: 2 hearts, 88/99, etc.I also like to second barrel the turn vs loose players because they usually call the flop with anything.
A bet commits us to the pot. How much would you bet, 120k? then you would only have 100k behind. I prefer to check.
I don't think 2 barreling with middle pair is a good idea. We would be putting too much money into the pot with a mediocre hand, and even vs a loose playing that's not wise.