Interesting that you should point out that one of the purposes of the Constitution was to support Militias. Does this mean that the interpretation that heavy arms should be reserved for “a well regulated militia” and that lighter arms are suited for individual hunters and home owners is the correct one?
The "Militias" were not a creation of the Constitution. They were made up of people from the various states. In order to insure that they be "well-regulated", that is proper functioning, the federal government was prohibited from infringing upon the right of the people to keep and bear arms. ALL arms, not just "light arms". Private citizens at the time could be owners of perhaps the most powerful weapon of the time, the equivalent of a warship armed with cannon.
The existence of a standing army is no substitute for state Militias armed by the people of the various states. It was a standing army that occupied Boston prior to the Revolutionary War and the Second Amendment was ratified to insure that future Militias could prevent the central government from using such an army to tyrannize the people.
I am no expert on the subject, but I doubt if one could argue successfully for a right to private ownership of heavy ordnance.