I think your line is fine, and I would only raise at some point if I had a strong read on his actions, for example that he would play 6Q this way (in which case he's very bad and exploitable).

For most lags I think in this spot their range is pretty much polarized; they either check the flop because they feel the flop is too risky to lead into 3 people or because they have a monster. They will almost always lead out on the flop with a naked 6. So unless he's very tricky I say it's air or monster here, and a river raise doesn't do you any good.