In 1776 you COULD own a cannon.
In 1776 you COULD own mortars.
In 1776 you COULD own sniper rifles (that is rifled armies as smooth-bore was the standard infantry arm.)
In fact well past the CIVIL WAR, 1864 or so, you COULD own Gatling guns as well as cannon.
I don't think up the 1930s there were restrictions on machineguns either (except maybe in the liberal north.)
What is more several SCOTUS decisions pointed out the 2nd Amendment had a relationship to defending the country, and hence military weapons.
U.S. v. Miller, 307 U.S. 174 (1939).
This is the only case in which the Supreme Court has had the opportunity to apply the Second Amendment to a federal firearms statute. The Court, however, carefully avoided making an unconditional decision regarding the statute's constitutionality; it instead devised a test by which to measure the constitutionality of statutes relating to firearms and remanded the case to the trial court for an evidentiary hearing (the trial court had held that Section 11 of the National Firearms Act was unconstitutional). The Court remanded to the case because it had concluded that:
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.
Thus, for the keeping and bearing of a firearm to be constitutionally protected, the firearm should be a militia-type arm.
But earlier SCOTUS ruled that the rights to keep and bear arms as per-constitution.
United States v. Cruikshank, 92 U.S. 542 (1876).
This was the first case in which the Supreme Court had the opportunity to interpret the Second Amendment.
The Court recognized that the right of the people to keep and bear arms was a right which existed prior to the Constitution when it stated that such a right "is not a right granted by the Constitution . . . [n]either is it in any manner dependent upon that instrument for its existence."
And yet, people have questioned what does 'people' me (as in WE the People!)
United States v. Verdugo-Urquirdez, 110 S. Ct. 3039 (1990).
This case involved the meaning of the term "the people" in the Fourth Amendment.
The Court unanimously held that the term "the people" in the Second Amendment had the same meaning as in the Preamble to the Constitution and in the First, Fourth, and Ninth Amendments, i.e., that "the people" means at least all citizens and legal aliens while in the United States. This case thus resolves any doubt that the Second Amendment guarantees an individual right.
http://www.firearmsandliberty.com/fedcases.2nd.html#SC1
Does that mean I think everyone should have a A-Bomb?
No.
But does that mean with a through background check one can own a machinegun or even a cannon?
YES.
Deaf