You notice in the amendment it links "militia" and the right of the people to bare arms. In no way do I believe that the founders of the constitution meant the right only to extend to side arms. Weapons of war where meant to be included. Private ownership of large weapons of war was not that uncommon at least until civil war era. Your question becomes nonsensical when you talk about modern weapon systems simply due to the costs involved. Even Bill Gates probably couldn't afford to buy and operate an aircraft carrier.
I have a counter question for you.... Can you point to any part of the constitution that would grant the government the power to limit the peoples right in this regard?