When Byron Allenbought the Weather Channel for $300 million, in March, it might have seemed to some like the setup to a late-night punchline.

Byron Allen? The man who co-hosted “Real People” in 1979 and now appears on syndicated comedy shows?

Mr. Allen is serious, though. He paid cash. Without much notice, the former comedy prodigy has a built a privately held media company, Entertainment Studios, that owns eight cable channels, produces more than 30 TV programs as the U.S.’s largest independent producer of first-run syndicated programming, operates a film-distribution company that spent $16 million to promote this month’s release of “Chappaquiddick,” and is planning to expand.

“They’re a hungry company,” says Mark Ciardi, a producer of “Chappaquiddick.”

Mr. Allen, 56 years old, owns 100% of the Los Angeles-based company. “It wasn’t necessarily by design, but it ended up being that way when you don’t have people who are interested in investing,” he says.