This is one of those questions I wish I had a time machine for ten minutes. I'd like to clarify with the Founders what they meant.
There were firearms in that day that could not be carried (say, a 6 pounder cannon; it had to be wheeled around, usually by horses). If someone were to ask George Mason, Patrick Henry or James Madison if a normal citizen could keep a 6-pounder in his house, I reckon they'd look at you and say the eighteenth century equivalent of "You're a special kind of stupid, aren't you?"
On the other hand, the Virginia Bill of Rights of June 1776 covers the matter this way: "That a well-regulated militia, composed of the body of the people, trained to arms, is the proper, natural, and safe defense of a free state; that standing armies, in time of peace, should be avoided as dangerous to liberty; and that in all cases the military should be under strict subordination to, and governed by, the civil power."
Obviously, firearms are not protected because they are useful for sport shooting, hunting, but are intended to allow the people to protect themselves against abusive government (and also probably protection against Indians). If the government has improved weapons, the idea that the people would have improved weapons as well would not seem altogether strange to Mason and the Virginia Founders.
How far they would have gone is a good question. If the Brits had used bolt-action rifles 1775-1783, would the Founders have allowed citizens to "keep and bear" them? If the Brits had used magazine-fed semi-automatic rifles?
The two things I am sure about are these. The Founders, if questioned would say, "We left you an amendment process. Use it." Second, they would say, "absent an amendment, the general government must remain within the limits we set up for it."