Are "military grade" weapons covered by the right to keep and bear arms?

Text of the Second Amendment: "A well regulated Militia, being <<necessary to the security of a free State>>, the right of the people to keep and bear Arms, shall not be infringed."

In 1939, the Supreme Court of the United States in Miller [full case citation below] denied the claim of a defendant that certain provisions of Federal law regulating the possession of certain firearms was Unconstitutional. The reason the Court denied the claim is crucial to the current debate over Federal and State regulation of firearms, and the meaning of the Second Amendment according to the Supreme Court.  [By the way, the Heller decision did not overturn or modify the decision in Miller, which therefore remains binding precedent. The two decisions are completely compatible.]

To understand the Court's decision in Miller, one must first comprehend how the Miller Court interpreted the Second Amendment:

The Constitution, as originally adopted, granted to the Congress power --

“To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions; To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress.”

With obvious purpose to assure the continuation and render possible the effectiveness of such forces, the declaration and guarantee of the Second Amendment were made. It must be interpreted and applied with that end in view.

The Militia which the States were expected to maintain and train is set in contrast with Troops which they [p179] were forbidden to keep without the consent of Congress. The sentiment of the time strongly disfavored standing armies; the common view was that adequate defense of country and laws could be secured through the Militia -- civilians primarily, soldiers on occasion.

The signification attributed to the term Militia appears from the debates in the Convention, the history and legislation of Colonies and States, and the writings of approved commentators. These show plainly enough that the Militia comprised all males physically capable of acting in concert for the common defense. "A body of citizens enrolled for military discipline." And further, that ordinarily, when called for service these men were expected to appear bearing arms supplied by themselves and of the kind in common use at the time.

Blackstone's Commentaries, Vol. 2, Ch. 13, p. 409 points out "that king Alfred first settled a national militia in this kingdom," and traces the subsequent development and use of such forces. ~ United States v. Miller (No. 696) 26 F.Supp. 1002, reversed. [Decided: May 15, 1939]

If that's how the Court interpreted the Second Amendment, then why did it deny the defendant's claim that the Federal laws regulating firearms at the time were Unconstitutional?

The reason was clearly not, as has often been falsely claimed, that the Miller Court concluded that the Second Amendment did not grant an individual right to keep and bear arms.

Instead, the Court explained its reason this way: 

In the absence of any evidence tending to show that possession or use of a "shotgun having a barrel of less than eighteen inches in length" at this time has some reasonable relationship to the preservation or efficiency of a well regulated militia, we cannot say that the Second Amendment guarantees the right to keep and bear such an instrument. Certainly it is not within judicial notice that this weapon is any part of the ordinary military equipment, or that its use could contribute to the common defense. Aymette v. State, 2 Humphreys (Tenn.) 154, 158._

In other words, no evidence had been entered into the official record of the case proving that the weapon possessed by the defendant (a shotgun with a a barrel length of less than 18") was "any part of the ordinary military equipment, or that its use could contribute to the common defense.

The Court interpreted the Second Amendment as protecting an individual right to keep and bear military grade firearms, and as far as it knew based on the evidence presented, a short-barreled shotgun was not "ordinary military equipment," nor was it useful for the common defense of the nation.

So the defendant lost the case solely because his firearm wasn't--in the opinion of the Court in the absence of any evidence on the subject in the official record of the case--a military grade weapon useful for "the common defense."

Therefore, per current binding Supreme Court precedent, any outright prohibitions of firearms that qualify as "ordinary military equipment" or that would be useful "for the common defense" are Unconstitutional.

As for the semantics of the fact that the Constitution uses the term ‘militia,’ here are some relevant facts:

“I ask, Sir, what is the militia? It is the whole people. To disarm the people is the best and most effectual way to enslave them.” ~ George Mason, said during Virginia’s Convention to Ratify the Constitution, 1788; George Mason as the co-author of the Second Amendment

"What, Sir, is the use of a militia? It is to prevent the establishment of a standing army, the bane of liberty .... Whenever Governments mean to invade the rights and liberties of the people, they always attempt to destroy the militia, in order to raise an army upon their ruins." ~ Rep. Elbridge Gerry of Massachusetts, I Annals of Congress 750, August 17, 1789

"The project of disciplining all the militia of the United States is as futile as it would be injurious, if it were capable of being carried into execution. A tolerable expertness in military movements is a business that requires time and practice. It is not a day, or even a week, that will suffice for the attainment of it. To oblige the great body of the yeomanry, and of the other classes of the citizens, to be under arms for the purpose of going through military exercises and evolutions, as often as might be necessary to acquire the degree of perfection which would entitle them to the character of a well-regulated militia, would be a real grievance to the people, and a serious public inconvenience and loss. It would form an annual deduction from the productive labor of the country, to an amount which, calculating upon the present numbers of the people, would not fall far short of the whole expense of the civil establishments of all the States. To attempt a thing which would abridge the mass of labor and industry to so considerable an extent, would be unwise: and the experiment, if made, could not succeed, because it would not long be endured. Little more can reasonably be aimed at, with respect to the people at large, than to have them properly armed and equipped; and in order to see that this be not neglected, it will be necessary to assemble them once or twice in the course of a year." ~ Alexander Hamilton, Federalist Papers #29

One of the delegates to the Continental Congress, explaining the meaning and intended effect of the [then proposed] Second Amendment: "As civil rulers, not having their duty to the people before them, may attempt to tyrannize, and as the military forces which must be occasionally raised to defend our country, might pervert their power to the injury of their fellow citizens, the people are confirmed by the article in their right to keep and bear their private arms." ~ Tench Coxe, Philadelphia Federal Gazette, June 18, 1789