I think one's view on whether or not the banning of certain weapons is constitutional is dependent upon what that individual believes the purpose of the Second Amendment is. There have been arguments made that it was perfectly lawful to privately own a fully functional cannon until just a few decades ago.
If you believe that the Second Amendment is there to allow citizens to have some sort of defense against a tyrannical government, then you probably are of the opinion that at least some weapons which are commonly considered "military" should be allowed. If you believe it is there to allow a citizen to protect their self from home invasions and to defend their home, or hunt with, then you probably see no point in owning larger or more powerful weapons.
My personal opinion is that if the weapon is incapable of killing and/or injuring more than five unfortunate souls with one discharge (a shotgun with scattershot for instance) during its average usage, then it should be allowed to be privately owned. Something more powerful should not be allowed because the average citizen would not be able to protect their self against such a weapon (maybe 1 in a 100 would have the resources to buy such a weapon), and it would be giving too much power to any one person or group.
Then again, I am also one who is of the opinion that if someone is intelligent enough to manufacture something on their own, there isn't much point in outlawing the ownership of it (sales yes, ownership no). The fact of the matter is, that if they want it bad enough, and they have the mental capacity to make it as well as the resources, they are going to have it. How do you stop that? You can't!