In the dream sequence early in the film, Hank's hose is made weightless by a string, and Paxton's glove is pulled off by another one. You can see them.
None of the weightless scenes were shot using strings, as far as I know. I haven't been able to go back and watch the scene, but I know that most of the weightlessness scenes were actually shot in zero-g on NASA's specially modified KC-135 tanker, lovingly known as the "Vomit Comet".
The director, Ron Howard, notes on the DVD commentary that the dream sequence was shot specifically to look unreal (because it was a dream). To get this effect, the scene was shot on the ground using traditional movie-making tricks to mimic zero g - it definitely was not shot in the "vomit comet". When compared to the "real" zero g scenes, I think it achieves the faked look that was intended.