Not sure preflop is it good to call because of kicker. But one advantage for calling is that BB fish can enter the pot.
On flop it looks like BTN is not having strong hand because of sizing. So I think with nut FD raise is better, because for calling we need implied odds.
On turn we don't know if he will barrel here, but when we donktbet it might look strong on such board, so nothing is left - only let him bluff or value bet Ax.
River - I think is ok, because we did not bet the turn so showed weakness, not he might not give as much cretit as on turn and call.