"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."
-- Second Amendment to the US Constitution
There is a good argument to be made that the 2A provides for members of the militia to keep and bear Arms without actually owning them. This would be similar to Switzerland's militia system (, in which (almost) all adults are issued a regulation weapon by the government. There were instances in the early Republic in which Congress appropriated funds to arm militias, and certainly the United States retains ownership of the arms issued to the National Guard today.
People who had just gone through a war against the most powerful military on the planet weren't going to trust a government with all the guns.
Plus, all the Bill of Rights did was list some things that it was illegal for government to ever do. If you look at the writings of those who wrote and signed the Constitution it is clear they knew the right to keep and bear arms (own and carry weapons) was superior to any government "laws" and pre-existed any government.
Also, the contemporary writers made clear that they understood "the militia" to be all men between certain ages (the ages where the ability to fight would be most developed and useful), and that it had nothing to do with being employed by government, and certainly didn't hinge on being under government control.
The Second Amendment didn't give any rights, it took away illegitimate government "authority".