No, I understand weightlessness, but I also understand English. The original article said:

He intends to climb into the pressurized gondola of the 650-foot balloon, which resembles a giant jellyfish, and make a two-hour journey to 130,000 feet. At that altitude, almost 25 miles up, Fournier will see both the blackness of space and the curvature of the earth. He will experience weightlessness.

Then he plans to step out of the capsule...
It has since been edited/corrected to say:

He intends to climb into the pressurized gondola of the 650-foot balloon, which resembles a giant jellyfish, and make a two-hour journey to 130,000 feet. At that altitude, almost 25 miles up, Fournier will see both the blackness of space and the curvature of the earth.

Then he plans to step out of the capsule, wearing only a special space suit and a parachute, and plunge in a mere 15 minutes, experiencing weightlessness along the way.
...with the following correction:

Correction: May 26, 2008

An earlier version of this article misstated the time in which a high-altitude parachutist would experience weightlessness. It is experienced during the descent, not while in the balloon's gondola.
Context is everything.