I beat Weiss this morning without materia or weapon upgrades maxed. There are some good tips from other people here but these are some random things that helped me:
I held onto my summon so that I could use carbuncle when he does immaculate end. This revived everyone even if they’re all knocked out.
You might get limit breaks earlier but surviving immaculate end with carbuncle gave every character a limit break. I saved Tifa’s and Cloud’s limit breaks for when he goes into his red lightning phase because I hated that phase and if you can hit both limit breaks then it puts him into stagger.
I used Ray of Judgment and Unbridled Strength to raise his percentage when staggered. Compared to some videos I don’t think I maximized my potential damage during stagger but it was enough.