It really doesn't. The federalist papers were an argument for the Constitution, without the Bill of Rights. The Bill of Rights were intended as a restriction on the misuse of the powers of the new government. Being amendments, if there is a conflict with the main body, the amendment rules. Thus all the "interstate commerce" BS used to justify gun regulation/laws, is such much horse puckey. "Shall not be infringed" means just that. Even in the context of exercising powers granted to the Federal government.
I'm not so sure of this. The Constitution itself is supposed the limit the powers of the federal government, delegated to it by the Several States, and the People. The Bill Of Rights was supposed to be a declaration of the powers that remained with the People and the Several States, rather than a limit on the Federal Government.
In other words, instead of saying that the Federal Government had all powers except for what's in the Bill of Rights, the Bill Of Rights was trying to say that the People and the States kept all powers except for what's in the Constitution.
Also, why all the talk of militias in the Federalis papers if the only mention of militias is in the Bill Of Rights?
-PJ