Paratroopers of the U.S. Airborne Forces (such as the 82nd and 101st Airborne Divisions) sometimes had extra pockets added to their standard uniforms to carry more equipment on their parachute jumps.
It was indeed a big risk though. Carrying extra equipment during a parachute jump had multiple implications and was carefully weighed. The paratroopers had to balance the need to carry enough equipment with the risk it posed during the jump.
The squad leaders were not always in favor of this, and looked at it on a person-by-person basis whether or not they then approved of it.