One of my friend played this hand in a smallstake tourney ( he's a plo fish )

we had a discussion about whether it's a bet or not

Blinds 2000/4000

Hero Stack 125000
villain got Hero covered

I dont remember exactly what happened with BB but lets say he was on "sitout"

Hero is BU with AK53

MP raises 4000
Hero calls 4000

Flop: K56
BB checks, MP checks, Hero ???

I think that a check is fine:
-we have a middle strong hand and dont want to get checkraised
-hands that are not calling a cbet are unlikely to improve on the turn, so there ist no risk of giving a free card
-when we show weakness villain maybe starts to bet with garbage
-we dont blow the pot with a hand that is also unlikely to improve much

would be nice to hear other oppinions

Hand is fairly off.
If bb is at 4K how can he raise to 4k?
Player in the bb is quite important... lol at „sitout“
I‘de bet this flop either if it‘s a raised or limped pot.

Quite an easy bet imo.

Lmao 2p:2nfd:bdnfd on this board is a "middle strong hand"?
Don't be such a ****ing nit.

wtf is up with the hand....

anyway apart from that your thought process is way off. Getting raised can always suck unless you have a nutted made hand/draw but by itself it's not a reason to bet because a lot of time you won't get raised and you want to put pressure on the part of their range that isn't raising you for value/protection.

Which leads on to your 2nd line of reasoning, which is just completely not true. There are many hands that SHOULD be folding to a bet that have decent equity vs our hand and can definitely improve on turns. These include non-nut FDs with no/little backup (eg. QJT8 with J high FD for instance) or OE straight draws with little else to go with them (78xx, 34xx, 74xx) - particularly the latter 2 where they are non-nut SDs where there outs could bring a flush.

We have a vulnerable made hand that is unlikely to improve but has value in a bet => it's an easy bet. The more free cards we give, the less likely we are to win the hand.

Now, when the inverse is true and the more free cards we get, the more likely we are to increase our equity - this is when you really DO hate facing a raise and can make a more compelling case for checking. Typically it would be when we have something like an OE and a back door FD but not much else. So a hand like 7sAs8T here would be a great candidate for checking back.