If he's used to you checking behind & folding the river when you give up on your steal, then fire again on the turn. He'll think you must have something because he's used to you folding.

Surely some of the times you quit & he bets on the river, you've got him beat (even with Q high). Similarly, some of the times you fire again on the turn, he'll be beating you. But, in my experience, you can't stop on the turn in 6-max if you're stealing but suspect BB is too (you said he auto-calls your steal). This increases the investment to stealing, but I'm betting you will find more success.

What % of the time do you win when stealing? I'm at about 70% and nearly 1 BB per hand in the black (or green rather), so you can gauge from there. I'm not sure what "ideal" is for these figures, so I'm posting mine to also hear other responses.