a9o on the bb in 2/4 six max

[Allday Everyday]

I think checking is correct preflop. If suited, it must be close to a raise IMO.

I think the flop check-raise is good only if you know there is a high likelyhood a LP player will bet. And given your description of the players I don't think we can say that here. So I would bet.

Given that you checked flop, yes, I'd value bet that turn.

I prefer a river bet-reraise to a sexy check-raise especially given that villain is probably passive and not likely to do an expert value bet-call or a bluff. Given the drawy nature of the board I think your check will induce a bluff from busted draw a small amount of time, but I think this is just a case of getting a call out of a calling station. Easy river bet IMO.