Were there weapons that a private citizen could not legally own in 1789 in the US?

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 early post colonial US there was very little "Federal" law. It was mostly local (town or county) or State law. There also was no real federal "Standing Army" until the Civil War. The only military weaponry of that day were canons, and by association, large stores of Black Powder. Many local jurisdictions prohibited civilians from possessing, in their homes, canons or large stores of black powder. In Marblehead MA there was a town based "Powder House' outside the Village where the local militia had to store it's black powder, and then transport it to the fort that guarded the entrance to the harbor. While this has little to do with restricting the ownership of weapons, but more likely implemented as a safety measure to prevent the town being leveled by an unintentional or intentional detonation of the gun powder stores.
The framers of of Constitution and the Bill of Rights (3 were from Marblehead MA) were also the same local leaders who enacted these local prohibitions against civilians possessing this military weaponry. It is hard to imagine Eldridge Geary or General John Glover approving of every Tom, Dick and Harry possessing the weapons of mass killing that an assault rifle with a 30 round magazine represents.

In a word: no. It was quite legal for private citizens to own, for their private use, any manner of weapons with which a vessel might be equipped to engage in maritime raiding and piracy privateering. During both the War of Independence and War of 1812 the U.S. relied heavily on the efforts and resources, both monetary and other, of private citizens for the pursuit of its naval war.

In both the War of Independence and War of 1812, the Congress authorized the granting of letters of marque to private citizens: commissioning them to operate their privately owned and outfitted naval vessels as maritime raiders; for a profit.

The only restrictions on these that I can find are:

• U.S. Constuitution Art I, § 8, clause 11:

  *The Congress shall have power …; To grant letters of marque and reprisal, and make rules concerning captures on land and water;

• U.S. Constitution Art I, § 10, clause 1:

  No state shall …; grant letters of marque and reprisal; …

• Procedure:

  • during War of Independence:

    During the American Revolution the Continental Congress adopted a printed form with blank spaces for the name of the vessel, owners and master, and figures for tonnage, guns an crew. These blank commissions, signed by the President of Congress, were sent out to the United Colonies, who assumed primary responsibility for the regulation and conduct of their own privateer fleets.

  • during War of 1812:

    By 1812 a shipowner applied in writing tho the Collector, or in some cases directly to the State Department. If approved, he would then sign a bond, usually for a sum ranging between $5,000 and $10,000 (depending upon the size of his vessel or crew) to insure his ship’s compliance with the conditions of the Letter of Marque or Privateer Commission. The document itself, containing the signatures of the President and the Secretary of State, was then issued to the shipowner through the Customs Service, and remained valid until recalled by the government or canceled through a violation of the bond.

In all cases it must be emphasized that the letter of marque was not a license to own all manner of weapons with which a privateering vessel might be equipped, including not only muskets but 32lb cannon and 64lb carronades, cutlasses, etc. – as the vessel must have been fully outfitted prior to applying for such – but to sail the high seas and privateer against the nation's naval foes.