Well,
Spellweave is triggered by Kalecgos' presence
Spellweaver, which states it can proc from both attacks and spells.
Additionally the
Dungeon Journal entry for Spellweave states that it only damages enemies within 6 yards that are not your current target.
I'm not so sure on either restriction though. I don't know about the exclusively other mobs part, but I regularly see my Spellweave fly off to other platforms. We're doing 3-1-2-4, and by passing over the second plattform, I get a few attacks on it which seem then to trigger the Spellweave later on.
Maybe the 6y limitation really only matters when you first attack a target, and doesn't later on (because it's already on your "eligible targets" list or whatever). If that's the case you could cheat more procs by bunny hopping on all platforms and attacking each tentakle there, before returning to your original target and continuing the fight as normal. Maybe something to test in the next LFR raid.