This is "Peter Graves" by William Pene du Bois. The anti-gravity material is called Furloy.
It's a short book though, not a short story. Published in 1950. My copy is from 1972.
The cover image shows the harness you mention (with golf club head covers holding the Furloy balls, and a fishing rod safety tether).
And here's a scan of an interior illustration ...