Do you kill with weapon u want to recharge?
Yup. Every time I get the "not enough charge" for the weapon, or if it does have a charge I never notice it go up. Mind that this is with a petty soul charge, so I should notice something if it was working.
It should recharge if your weapon deals the final blow, not poisons/companions/magic.
Maybe companions might be doing the deathblows, but even then I know I have gotten some kills with just the weapon. Perhaps the 5% is so insignificant that it is unnoticeable?