I think it's been officially stated, that the class per job is 1-1. So PUG=MNK, MRD=WAR, GLD=PLD...etc...
So if the system is that basic, then weapons for jobs must be equal to the class that unlocks them.

Unless which I hope in theory is what they do, treat classes as requirements to unlock jobs, but treat classes as the weapon levels for jobs.

So for example, Warrior can use Great axe, Sword, H2H, and Lances. To level the Warriors efficiency with those weapons, would require the Warrior to level the class that is connected to those weapons.

Kinda similar to ffxi's versions of skilling up weapons. However, weapons(or classes) still have the ability to play as independent units.