Never tried it, but I'm pretty sure the Weakened Soul effect only happens inside the soul cairn. Right before you go in after Serana soul traps you, it says weakens soul added, but nothing shows up in the active effects menu. It only gets added once you go in. Of course it could stick around once it's been activated, but again, never tried it.
Didn't notice any weakening either in or out of the Soul Cairn, still got a chunk of soul missing... but I'm too impatient to spend anytime in the Cairn looking for it. I guess my character has been soul weakened for over 20 playing hours now & it all seems fine.
I never did get it back and have not noticed any ill effects without it. The Soul Cairn was a boring, desolate place and like other players have said, I do not want to go back there again.
Soul Cairn was a flippin [censored]. Okay. I am serious. I tend to use the map and am not a big fan of the quest markers, but the map so damn flippin useless in the Soul Cairn and there were no reference points to position myself I was running around the flippin Soul Cairn for god who knows how long just to gtfo there. I happened to accidentally find my full Soul Gem. I hate the Soul Cairin never going back.