Harrison's intelligence comes from Hazel, not George.
Diana's reason for her equality-crazed dystopia: Her own cripplingly handicapping guilt at having been a child prodigy, while her sister was mentally retarded. Her sister's name: Hazel Glampers-Bergeron.
The original short story is a Future Imperfect retelling of the film.The hyper-equality of the world eventually breaks down, due to a generation of people growing up with the legend of Harrison Bergeron. The constant praise of his actions lead to his becoming an immense Memetic Badass to the point where the fable of Harrison Bergeron more resembles the fantastic events of the story than the (relatively) mundane events of the movie. Stealth Parody.
This is the same universe as The Screwtape LettersScrewtape Proposes a Toast to a trend that looks to end with the scenario in HB.
Harrison is so strong because he's had to carry those weights all the timeThat's it, really.
Harrison "flying in the air" was just a misunderstanding by the viewers.Since the story's world is based around the idea of bringing everyone down to the lowest common denominator, what would be considered "normal" abilities would be very minor in real life - Harrison may have only jumped several feet in the air. Though, this does leave the mention of "kissing the roof" out of the picture...