Around 1800, private citizens owned cannons, which were pretty much the top-of-the-line military technology at the time. (At a minimum, there were privately-owned merchant vessels with cannons.) So at least at that time, there were no limits.

This does not mean that I am in favor of private citizens today having nukes, or even howitzers. I'm just saying, at the time of the Second Amendment, it was more or less unlimited.