Against an unknown, I'd check/raise this flop with the intention of bet/folding the turn.
This does two things -
1. Establishes a history with the villain.
2. Folds out unimproved hands that beat us, and lets us represent the Q.
His flop bet is lame. Sure, it's a big blind, and we like getting BBs. But if we're in this pot out of position with A8o, well, what the hell were we hoping for? We've already called with a loose range, we might as well play this pot aggresively to try and take it down with 2nd pair Top kicker with some tricky play on the flop.
In my opinion, loose passive is bad, we are not likely to get paid off when we improve because we establish a history of check/calling until we have a hand we believe best, then once we start betting and raising it is obvious that we have improved.
This is the easiest player to avoid dumping to, especially if you have a read on them like "doesn't bet with less than top pair or an overpair." One of the players at my live game out here is like that, and I took his stack about four times last night.