I'm a boss of devs. My off the cuff response to you is "please, god _please_, talk to your boss."
Say exactly what you told us. "I'm burnt out, I've tried addressing the problem..."
Before you do, think through what's causing the burnout. It could be the hours, that's where everyone goes first, but it could be a particular client, it could be the number of projects you're having to concurrently work, it could be your environment, it could something else completely, or it could be a combination of a bunch of those things.
Once you get sorta close to what's causing the burnout you can work to a solution that you can pitch your boss. But I wouldn't lead with it, I'd let him ask you "so what can we do" and then present what you're thinking.
Speaking as a boss, I really don't want people quitting for negative reasons. If they get some crazy offer that I can't match or they get to work on some cool tech that excites them, them's the breaks and it suck for me but I'm excited for them. But if I have people quitting for systemic reasons, man that's bad juju and I need to know so I can fix that shit before quitting becomes contagious and I lose a shop full of good people.
It's also been mentioned a couple times to see a counselor. I concur. You may be dealing with some anxiety and depression issues that a qualified doc can help you through.