Actually, it means any weapon that an infantryman might carry; not a weapon of mass destruction.
Which in turn doesn’t explain why for the first 120 years or so of this country’s existence, private citizens were allowed to own the weapons of mass destruction of their day - fully armed and armored private naval craft, some of which rivaled the battleships (ships of the line) of the day. See the East Indiamen merchant ships - some could see off first-rank ships of the line and lay waste to coastal cities with their armament - yet individuals could and did own them.