I am not entirely sure of the exact workings, so part of this post is guesswork. But like Rodeo, Counterbalance affects the base recoil mechanic without altering the stability stat. Stability only affects the recoil based ok that base stat.
Rodeo lessens the left and right kick of the recoil, making weapons with Rodeo mostly kick upward. Stability will then affect how much upwards it kicks.
Counterbalance I think is a general buff that lessens the base recoil, again without changing the Stability. Stability bonus is then applied on the altered base recoil.
It could also be faster re-centerspeed, meaning the weapon returns to the default position quicker after kicking.
Not sure exactly how Counterbalance works, but I know those two affect recoil separately from the Stability stat.
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Having played since day 1 and having a swarm with counter-balance, I can most assuredly tell you the stability bar is (supposed) to be impacted. When I activated this perk in week 3 of destiny's launch on my swarm, the only thing which produced a larger boost to the stability bar was perfect balance. Now, as of this month, I'm seeing it does nada when activated. (the swarm in question has retained it's expanded stability, however, which I find odd)
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I am not sure like I said, of the exact workings. But last time I activated a Counterbalance, the recoil was lessened (and it felt lessened), but still the Stability didn't change. Rodeo is exactly the same manner. Much less horizontal recoil, but kicks about the same vertically. I think Counterbalance lessens the recoil in all three directions, but less per direction than Rodeo does left and right. [b]I think![/b]