Weaver Dual Attacks feel weak and useless half the time. The elite spec is basically designed around using your dual attacks as much as possible with at least 4 traits specifically tied into them. I shall now list the skills by impact.
Heavy Impact Skills:
Staff: Pile Driver
Scepter: Earthen Synergy, Plasma Beam
Dagger: Steam Surge, Katabatic Wind, Mud Slide
Sword: Gale Strike, Lava Skin, Pyro vortex
Medium Impact Skills:
Staff: Pyroclastic Blast, Plasma Blast
Scepter: Fiery Frost
Dagger: Grinding Stones, Ashen Blast
Sword Skills: Natural Frenzy
Low Impact Skills:
Staff: Pressure Blast, Lahar, Monsoon
Scepter: Glacial Drift, Fracturing Strike, Stone Tide
Dagger: Plasma Burst
Sword: Shearing Edge, Twin Strike
Some of the skills in the medium and low categories have aspects which are useful in pvp but are either too slow, clunky, or don't provide what you actually WANT when attuning to that attunement. For instance, most of the skills you will notice in the bottom category have water as part of their attunement combo. When an elementalist switches to water, they want a skill that will heal them or otherwise offer sustain far greater than being in Air-fire for instance. Staff and scepter are the most egregious in this regard. On staff, I am sacrificing a potent aoe heal for skills that, what, do weak damage and apply weak conditions?! Seriously. As for Scepter, Glacial Drift and Stone Tide are just AWFUL. Good luck being effective with either of those. I know Water Trident doesn't heal much, but it can at least cure a condition when traited. I could go on and on but I think weaver seriously needs to be looked at.
On a side note
Traits which reduce the cool down of skills in a specific attunement should function for Dual Attacks as well. If both are taken, they should double up to be a 40% CD reduction. If this means increasing the base CD of some dual attacks so be it.