It starts from the foundational document, the
Declaration of Independence:
We hold these Truths to be self-evident, that all Men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness
We have rights to life and liberty, and the right to private ownership of weapons acknowledged in the 2nd Amendment is an instrumentality to help ensure that. It should also be noted that the Bill of Rights (1st though 10 Amendments) were a price demanded by the Anti-Federalists for accepting the Constitution.