There is no requirement for "a license and register the weapon" in the 2nd Amendment to the Constitution.   None whatsoever.  Please note the "must issue a license" language from the US Supreme Court.

District of Columbia vs. Heller "The District’s total ban on handgun possession in the home amounts to a prohibition on an entire class of “arms” that Americans overwhelmingly choose for the lawful purpose of self-defense."

 "Assuming he is not disqualified from exercising Second Amendment rights, the District must permit Heller to register his handgun and must issue him a license to carry it in the home."

Chicago v McDonald
"A City ordinance provides that “[n]o person shall . . . possess . . . any firearm unless such person is the
holder of a valid registration certificate for such firearm.” The Code then prohibits registration of most handguns, thus effectively banning handgun possession by almost all private citizens who reside in the City." 

This was found unconstitutional.