I want to know what we would do with A8s - A2s, KK, and QQ in this situation. I can see arguments for betting and for checking:

Betting: It is multiway, going into check/call mode with the middle of our range is tough because we will not realise our equity very easily so we can't really call much. We also pick up the pot against hands that might start bluffing us later, and we should get some folds because our range is stronger for betting mw. (This would just mean we are betting most of our range on this flop and when we check we are rarely continuing.)

Checking: Betting would turn our hand into a bluff effectively, we can't barrel turns unless we hit nutted, this board texture hits everyone's range quite nicely so betting gives us little FE and we will find ourselves on the turn quite often and have to check/fold after investing quite a bit.