The answer is no there is no such line not in the constitution and not in the practice at the time it was written.   People owned and operated warships (bigger and better than the US navy ships I might add).  Owned supplied and operated military like units with their own top of the line equipment including artillery rifles and muskets.   As soon as you start infringing on rights like that its only a matter of time before it goes away.   And we've seen that steady creep move more and more toward outright bans and defacto bans wherever the courts would allow it.