The name of the short story is "It's a Good Life" and it was written by Jerome Bixby. One word: telekinesis
I remembered that Billy Mumy played Anthony in the Twilight Zone episode, so I checked out his page on IMDb.com and found it there... along with the name of the writer.
"The Twilight Zone" It's a Good Life (1961)
The short story is well worth checking out if you ever get the chance. I remember the opening scene has a grocery store delivery boy on a bike coming to the house. He speaks to Anthony but is very afraid of him because everybody in town knows about him.
Anthony decides he doesn't like the guy... so as he rides away, Anthony accelerates the bike to some bizarre speed and the guy screams as it disappears down the street with autumn leaves swirling around in his wake.