You only get 6 as far as I can tell. I suggest these weapons in this order:
Dagger for Laka > Spear for Vahn/Adder > Mythraven(sword)/Balmug (darksword)/Ninja Blade/ Abraxas(wizard staff) depending who you use most.
The Axe and Rod have comparable or better ones available in side content and the bow is meh. The hammer could be good for Cid, if you use him a lot.
The ones used by the most characters are the Dagger, Spear, Wizard staff, and Sword.