So, regarding the fighter jet and nuclear warhead, it is not considered a man-portable arm, which the supreme court has narrowed the definition of firearm down to.
There are arguments for and against whether or not it ought to be absolute, but clearly it is not, at least as presently governed. Thus far, the only known challenge on the National Firearms Act (which is what prohibits us from buying fully automatic machine guns) was US v Miller, in 1939. That was, as I mentioned in another thread, a very curious peace of legislation because Miller, a known gangster caught in possession of a sawed off shotgun, was being tried for possession of something he shouldn't have. He argued that per the second amendment, he should have the right to carry it, as it would be useful in the aid of a militia.
There were some challenges in transportation, and portions of the trial were run with Miller in absentia, during which time the US Government testified that sawed off shotguns had never been useful to the army, and should not be considered useful to a militia -- despite the fact they had been in use somewhat regularly only 20 years prior, by the US military. Further, Miller was killed before the decision was rendered, but the trial went on.
So, that said, if one believes that what the Supreme Court deems is Constitutional is, in fact what is Constitutional, then we are subject to 'reasonable regulation'.
Looking more recently however, at DC v. Heller. At the time, DC's laws had an outright ban on handguns, and as such, prevented him from doing so. Heller was a security guard at a Federal building during the day (where he was armed), but went home at night to a very bad neighborhood with no means to defend himself. He petitioned for the right to bear arms, and ultimately, the decision was found that DC's outright ban on handguns was unconstitutional, and was struck down. In the majority opinion, Justice Antonin Scalia claimed that weapons "in common use at the time" were exempt from outright bans.
More recent cases since Heller have pretty much affirmed this, with bans in Chicago (Chicago v McDonald), Illinois (Moore v Madigan) and others being outright struck down as unconstitutional. Similarly, I believe that attempts to ban the AR15 (and similar popular weapons) will, if successful, be ultimately struck down as unconstitutional per the precedent in Heller. The AR15 is the most popular rifle sold in America today, and has been for a number of years, and is clearly "in common use at the time".
Regarding fully automatic machine guns, the NFA provisions have not been challenged since Miller, which wasn't even a full challenge in and of itself, and certainly went far above 'unusual'. I suspect that within the next 10 years we'll see someone challenge the National Firearms Act restrictions, and quite possibly win.
The reason I believe this is because the second amendment is provided "for militia" purposes and for "defense against tyranny, foreign or domestic." As it stands, we are far outgunned by our own military. Historically, the arms used in the Revolutionary War were almost entirely provided by the citizenry and militia men. Militia members were expected to show up ready to fight and armed with weapons "in common use at the time." That's where we got our rifles, but it's also where we got our cannons, mortars, ships and navy from -- all were provided by the citizenry at large.
That said, since I think you were asking my personal view, I can't say whether or not it is or is not unconstitutional, because it has not yet been challenged on Constitutionality. I know that might seem like a copout, and I suppose it is, but as there isn't particularly clear evidence either way, I would say that I dunno. The biggest argument for it, right now, is that there are legally ownable fully automatic machine guns (interestingly enough, the densest ownership of them per capita exists in New Hampshire, which consistently ranks between the 1st and 3rd safest states to live in) by paying a $200 tax stamp. I don't honestly feel that automatic weaponry has advanced in technology all that much, so if it makes sense that people can own old ones, why shouldn't those same people be allowed to own new ones?