As the question asks. I didn't really think about it at the time and just remembered after visiting Cid that they're upgradeable and unique. Is there any way for me to recover the machinery weapons I sold?
I kept the circular saw but sold the bioblaster and the autocrossbow.
Best Answer
Short answer: You cant get them back until you start another game, whether NG+ or otherwise. Personal notes below are in italics below the section header.
From to the Official Deluxe Ed. Guide (p.202-p.207):
Upgraded by Cid
Only the machinery can be sold with none of them can be bought back after being sold. None of the melee weapons in this list can be purchased in a store, only found or acquired during a quest / side-quest.
These weapons are carried over to NG+ in their current state at game conclusion with the exception of Ultima Blade, which reverts to Engine Blade III. However, all weapons carried over also duplicate in NG+ as if they were never acquired and can be re-upgraded and then sold allowing the player to sell and keep the weapon at the same time:
Collectible Only
These can be sold but not bought (there are collectible weapons that can also be bought, but the below list cannot) If you sell them, they're gone (sorry).
Pre-Order Bonus Only
These cannot bought or sold, do carry into NG+, and do not duplicate.
All other weapons can be purchased, sold, and repurchased.