to me, this passage at the end of the decision is key:
"Second, the right to bear arms is a protection against the possibility that even our own government could degenerate into tyranny, and though this may seem unlikely, this possibility should be guarded against with individual diligence. Third, while the Second Amendment thus stands as a protection against both external threat and internal tyranny, the recognition of the individual’s right in the Second Amendment, and its incorporation by the Due Process Clause against the states, is not inconsistent with the reasonable regulation of weaponry. All weapons are not “arms” within the meaning of the Second Amendment, so, for example, no individual could sensibly argue that the Second Amendment gives them a right to have nuclear weapons or chemical weapons in their home for self-defense. Also, important governmental interests will justify reasonable regulation of rifles and handguns, and the problem for our courts will be to define, in the context of particular regulation by the states and municipalities, what is reasonable and permissible and what is unreasonable and offensive to the Second Amendment. "