With that logic we could have nuclear weapons. There have to be some sort of limits.
Careful. The nuclear weapon argument is the preferred strawman of the Brady crowd. Assault weapons are a thousand orders of magnitude more discriminating than any weapon of mass destruction. I can defend my home with an M-16 or a Mac-10 without violating the rights of my neighbors. It may be more difficult to do than with a .22, but it can be done. Whereas, it would be impossible not to violate the rights of everyone within 20 miles of my nuclear weapon.
Not really. "Arms" as used in the vernacular of the 18th Century generally referred to the weapons carried and used by individual soldiers. Heavier weapons were generally referred to as 'Ordnance'. Under that common interpretation, citizens would be fine carrying the small arms of the day, but hauling around a MOAB, a Minuteman II or a Mk61 would not be acceptable.
Of course, if I found the guy strong enough to carry a MOAB on his own, I probably would not run over and yell at him; he might drop the thing on my foot!