1/2 NL, typical loose passive baddy table, 7 players.
V is big blind with about $300
H is UTG+1 and covers BB

There's a button straddle, which means there's $5 on the button, and small blind is first to act.

Hero has Ad Th

SB calls, BB calls, UTG folds, H Raise $25(trying to thin the post flop field), folds around, BTN calls, SB calls, BB calls. Great(/s), so much for thinning the field.

Flop: ( $100 )
JJ9dd

SB bets $10, which is actually typical of this nutty player, means weakness, BB calls, H calls, BTN calls.

Turn: $140
JJ97ddd

So far for ranges, I don't think I have any 99 to worry about, maybe J9, 77 could have got there.

SB bet's $20, BB raises to $40, hero?? I am getting about 5:1, looking for an 8 or diamond, BB could have a flush, Jx, and possibly a boat here.

What do we do?

Why did you raise so big in EP with a marginal hand?
ATo doesnt play so well oop. If it was suited im ok with the raise but I dont like this raise...
Flop: If you felt the donk bet to be weak, why dont we raise it and fold if they playback?
He bets 10 in 100, you can raise to 55 after BB has call...
This hand is pretty weird.
I fold pre. As played, no reason to call the flop, only giving out money. Raise or fold the flop imo.

Fold the turn after there is a bet and a minraise... min raise on turn at this limit is probably always the nuts lol.

Default preflop should be fold. If you do raise preflop then raise or fold on flop. With fewer opponents raising flop to carry through with representing an over pair might be OK after the weak donk. With this many opponents just give up. Not only is your hand weaker then you represented but there are lots of ways that your outs can be dirty so improving may just get you in more trouble.

In any case fold on the turn. BB may be exploiting the SB's weak bet but the risk that outs are dirty means it isn't worth it.