Ok, as far as I can tell, the special effect hit rate is tied to the current hit rate of your character wielding the weapon. Aim also influences this as well.
For instance, the Charm Claw has a putrid low hit rate, and that's pretty much why he has difficult inflicting the Charm status on targets. When combined with something that has a high hit rate (let's use the Cat Claw for example), Charm is more frequently inflicted with Sleep.
Also, enemy status hit rate seems to be tied to your evade rate. Unless enemies have some sort of hidden hit rate info that I should be aware of, the rate of infliction is truly tied to the evade rate. This is why characters like Cecil generally get hit by status effects, but less likely with someone such as Rydia who has the Heroine/Minerva Robe equipped.