Nope. For one thing, not all airborne were paratroops, as the term included glider troops as well. As for weapons, parachute troops had not only BARs but belt fed machineguns and light mortars as well. The heavier equipment was not carried by the trooper but was dropped separately by other chutes. The color of the chute told the troops what was in the attached containers - food, ammo, heavy weapons, commo gear, etc.