Moleendo Stewart can’t say for sure what’s caused his lifelong sleeping problems. But he has his suspicions.

There’s the childhood spent in loud, restless neighborhoods in Miami. “You hear people shooting guns all night, dealing drugs,” said Mr. Stewart, 41, who lives in the East Flatbush section of Brooklyn. He also cites his weight, 260 pounds, down from a peak of 310.

Sleep experts would point to another factor working against Mr. Stewart: He is a black man.