There were cannon in the days of the Founding Fathers. Were those included (either implicitly or explicitly) in the discussion of the “arms” we could keep and bear? Just curious.
The word "arms" has a fairly specific meaning, and that is personal weaponry carried by a foot soldier. Cannon and such larger weapons are more properly classified as "ordnance". I think the founders knew the difference and had they meant something beyond the "arms" of a soldier they'd have said it.
There's a practical matter to it as well. The militia was expected to keep and care for their own arms, and when the call came to muster... to show up with those arms. Logistically, treating the big stuff that way would have been awfully complex. Having all the larger ordnance bought and owned by the governor and kept and cared for down at the armory just makes more sense.