What size category are weapons if brought to life with the “Animate Objects” Spell?

A wizard at my table wants to use weapons (greatswords) for his Animate Objects spell. Do i take the weapons base damage and match it with the table of Animate Objects (2D6 making them Medium), or are there any rules i may have missed pertaining to the object-size of weapons?

Any clarification, or your own interpretation (if its up to DM’s) would be most welcome.

EDIT: After all your great informative input, I’m going with the following:

  • Weapons weighing 1 lb. or less as Tiny (daggers, darts and ammunition)
  • Heavy Weapons as Medium (glaive, greataxe, greatsword, halbert, maul, pike and h-crossbow)
  • All other Weapons as Small (unless indicated otherwise, oversized for example)