I have a weapon that has the ability to proc this effect already. If I added this augmentation to it, what effect would it have, would it double my chance to proc?
It is possible to add this augment to a procing weapon. However, in my experience you will receive at most 1 proc per weapon per attack.
Double attack = 2 attacks each with a chance to proc.
Weapon with 2 procs = 1 attack, 2 chances to proc, first to proc ends the proc check.
Think of it like this:
Rujarkian Stone Knuckles + Cobalt Crystal of Affliction = 2 chances to proc Rujarkian Mist.
You attack Proc check Rujarkian Mist (if successful apply effect and end the proc check, otherwise continue Proc Check) Rujarkian Mist (second attempt due to second proc) End of Proc check
My experience in this area is limited to using a proc capable weapon + a self buff that adds a proc. Augmentations may work differently, however, I would expect them to be the same until I see evidence to the contrary.
Parsing tests have shown that each proc on a weapon will get its own, separate chance to proc. Adding procs does not lower that chance of any other proc to proc. :)