For fully automatic weapons, it saves effort supporting a weapon that produces a lot of recoil. Rather than fighting gravity, it is working with you to hold the weapon down.
For small rifles, pistols and such, it would likely be preferable for the gun to fly over your shoulder rather than wind up pointing at your feet. Perhaps more importantly, human ergonomics lends itself to the arrangement where the barrel is above the wrist or shoulder; the opposite would be difficult to support with the additional of gravity.
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