Just thoughts on checking back?

Flop call is maybe even a little loose considering pre flop and flop sizing of bets?

But anyway when I'm check raised here i discount bluffs as they would keep barreling being out of position id imagine. So then i look at value hands i beat and only possibility is A10 which would also double barrel.

If my hand isn't good enough to be bet GII here should i be checking back? If I'm honest i was expecting a check call from AK but yeah that doesn't check raise was just a bit confused with what i should do there with all my range?

Obv bet GII with KQ but if I'm bet folding top two surely thats so exploitable i should be checking back?

Confused