Given the BB is seemingly recreational and passive I think I might personally prefer to flat this, see a flop and hit my Merry Christmas board. We get some protection from the BTN messing us about postflop because the BB is in the pond. If BB was more active I'd just fold preflop though.

Postflop I think you're more likely to be the dog here if your read is correct, I just wonder if a bet from us would be better, we have no real kicker and would rather get folds now than have them call and hit their 6 outs or whatever.

Just my ramblings is all.

Pre: Fine

Flop: I'd be more inclined to go ahead and bet here ourselves. If we get villain to fold a hand like JT/JQ/KQ etc that's OK, I would also expect villain to be checking back a decent chunk of their Ace highs on this board but will absolutely call at least one bet with their gutshot that is meaningless. When we do check, check jamming is my favorite option by far. We always have OK equity when called and taking down the pot now is a fine result also.

For the record, villain played his hand awfully. His flat pre is whatever, but his bet on the flop is just absurd, he accomplishes very little with a hand that has a lot of showdown value against your check fold range but is in trouble vs your check call/check raise range.