I'm not sure there is any law against owning an unarmed tank. But for "dangerous and unusual" weapons themselves, an important case is from 1939 - Miller vs USA. [1] And it's absurdly weird. Basically the defendant was a thug with a penchant for snitching on everybody.
In his final case, which he also snitched during, he argued that a law he had been charged under (a firearms regulation law) was unconstitutional. The judge who heard his case was very much in favor of the gun control law and had made numerous public statements as such, but he also likely knew that the law was on very shaky constitutional ground, and had been fishing for a test case to advance it. And he found that in Miller.
So he concurred with Miller about the law's unconstitutionality! That resulted in the case being appealed up to the Supreme Court. Conveniently for the state, neither Miller or his defense representation appeared. So it was argued with no defense whatsoever. And Miller was found shot to death shortly thereafter, which wasn't seen as particularly suspicious given his snitching habits. And that case set the ultimate standard that's still appealed to, to this very day.
This is made even more ironic by the fact that the weapon he was being charged for possession of as being 'dangerous and unusual' was just a short barrel shotgun, which was regularly used in the military.
> I’ve never really understood how the logic of the second amendment doesn’t extend to tanks and nukes.
Probably because if people could buy tanks to protect themselves, then the police would also need tanks to deconflict a situation where someone with a tank is upset and the damages are a bit higher when tank rounds start flying around. Imagine two neighbors getting into it in a a town, not to mention a city.
Even portable nukes are a stretch in the logic of "I need to protect my home" from intruders, not to mention the hundred kiloton yield ones.
The second amendment to the US Constitution doesn't concern itself with home defense justifications, but only with "we need to scare up a military force, right now". The "right way" to forbid tanks and tac nukes as arms that the people can own would have been to amend the Constitution with something that specifies the limits in some way, but instead we got creative interpretations of "shall not be infringed" to mean "can be infringed as long as a law or agency regulation is produced at either a federal or state level". Which is odd, as GP noted.
People can and do own tanks. Since they are giant (hard to park), slow moving, consume a lot of fuel, tend to need expensive maintenance, and can't be operated on many roads due to weight / vehicle restrictions, few people want to do this.
As far as nuclear bombs go... there are restrictions on owning fissile material in general that would preclude owning enough to have a working bomb.
