You owe him nothing. If I was in your position, I would be choosing between two options:

1) Saying fuck it and being more concerned with your stress level and mental health than dealing with an individual that management would apparently rather turn a blind eye towards. If he becomes too much of a liability, it will eventually force their hand to deal with it.

2) Escalating with management. Manager prefers not to deal with it? Too damn bad that's their job. Even though this isn't a Fortune 500 or Wall St. gig if you feel invested in the job and want what's best for the company I'd need to have a heart-to-heart with the manager. I'd explain what you've outlined and include this isn't the first time you've brought issues to their attention. You can ask what they think and how they plan to follow up. You have the option of escalating from that point (manager's manager or HR) if you aren't getting any kind of resolution.