How to defend on the big blind with A8s?

I think we are too deep to 3-bet shove here. This doesn't mean that shoving is necessarily -EV. It is not the most profitable way to play this hand imo.

I personally like calling here but would mix in smallish 3-bets. BTN range is big, we have an ace as an blocker and the hand plays okay even after getting called. I think good players will 3-bet this very frequently, but I don't think calling is too bad.

if he stacks of so loose 3bet shoving can be ok too. Most of the time I would flat in the BB too. On the flop I just fold. Peeling one street ace high is pretty marginal.

Well played. You want to have pretty polarized 3betring range from BB. Especially with stack depth that allows nice 4bet shove spot for villain.

A8s falls into mediocre strength hands that you might often want to 3bet from SB as calling has many issues. From BB it's different story and call is best play.

Flop you could call if you had backdoor flush draw but without folding is best.