A piece about 18 inches long. Wrap it around the base of the weights where the tape is, like a noose. Pull on the ends of the floss and it will cut through the tape.
After that, to get off the half-thickness of tape that's left stuck to the chassis and to the weights (or whatever it is that was taped to the chassis), use the pad of your thumb. Starting at one edge, push your thumb down onto the edge of the tape, while still pushing, pull the pad of your thumb across the edge of the tape. The tape edge will start to roll. Keep working / rolling that edge with the pad of your thumb, into a little bigger ... and a little bigger roll until the tape is all the way off!
The beauty of this method is neither the chassis nor the removed component get scratched up at all.