Spellweaving is a very defensive spell set and has a lot of utility spells. It won't do massive damage aside from word of death against monsters that are lower on life. It's mostly to enhance other spells, add in ways to avoid taking lots of damage, or "debuff" other players.
Attunment and Gift of Renewel are awesome for staying alive. These two spells alone justify getting a level 6 focus. Attunement will absorb some physical damage, making it really nice against archers/dexxers in pvp and most monsters in pvm. Gift of Renewel is a "dot" heal. It's really nice when you know your going into a situation where you will be faced with lots of damage. It also will cure poison, but if it does cure that is all you get out of it. I don't think the timer applies after you cure, but you need to recast in order to get the heals.
Gift of life is a self res, again very handy even more so if you play solo. You can also cast this on a pet, I've been dismounted, had my swampy killed, ressed it with gift of life and ran away. The problem is you have to cast the spell on the pet BEFORE it dies.
T storm and essence of wind are amazing in large fights but you seem to already know this, so I will say mix in wildfire also. It doesn't do much damage but has a huge area and it hits fast making it nice for a push or to interupt a large group of mages. Essence of wind is the best "debuff" spell in game next to curse. Slows swing speed, and increases casting times. It can be resisted, and appled out of if it does hit, but if you hit guys with this and they go to cast a high level spell they won't be moving for awhile. T-storm is FCR penalty, it's nice but I like wind much better. If two weavers are working together, one 'winds' while the other t-storms and no one is casting for awhile. Very effective this way.
Pixies/imps are just used to proc spell plauges or for interuption. They are very weak in hit points and don't cast high level spells. But both wildfire and pixies will proc spellplauge hits making it really nice if you can fit mysticism in or have a mystic with you. This is the main reason people will use them.
Natures fury is a low level summon that is pretty cheap in mana cost, it's mostly nice for a dexxer imo because they can get a few meatshields. These used to be awesome for pvp, you could fill a house up with them, but they fixed that.
Arcane Empowerment is the most underrated spell that spellweaving has imo. It increases the amount of damage you heal, taking a 50ish damage g heal to around 70-90. You will mini heal for like 25. It also will increase your gift of renewel damage healed. It increases the effectivness, hit points and decreases dispel chances for summons. Arcane Empowerment EVs are the way they used to be, and an AE Rising is just godly. This spell also increases your spell damage by a significant amount depending on your skill level and focus level. So this spell has uses for pvp and pvm. It's a tad heavy on the mana cost but it's worth it. Best spell that spellweaving has to offer, the ultimate buff for a caster.
Word of Death is a pvm spell, but it's a damn fine one. Does massive damage to an creature low on life. Used mostly for finishing peerless and champ bosses. The most I ever hit was around 750 damage, but on average expect around 350-500 damage. The suit I used to hit 750 was terrible and I bet a crafter could've killed me. This is the biggest reason people pick up spellweaving.
Certain other spells are just fun or have very limiting uses. Reaper form adds a little SDI and some swing speed but really isn't useable in most situations. Dryad Allure lets you "tame" a repond creature, but I've had issues with certain ones attacking me and since it takes followers you can't summon. Ethereal Voyage is basically like honoring yourself, but since it puts you on foot it again has limited use. I see this mostly used for things such as lady mel, when you go down to kill the satyrs. Immolate weapon has been broken for years, it's supposed to add some fire damage but it's so low that this spell just sucks. I don't know anyone who uses this..ever.
Now all these spells are scaled by the skill level and level of your focus. At 120 skill all spells will perform better then at 100 skill. 100 is better then 80, etc etc. So you can run 60 spellweaving, have attunment and gift of renewel but they won't absorb/heal the way it would at 120. The focus is the biggest factor, but 120 spellweaving has uses aside from a 99% chance to cast word of death.
But the biggest thing to remember with spellweaving is that it's not a main skill set. It's a support skill that enhances other abilites you may have. It's a lot like necromancy in this way, you can't make a necromancer and just rely on those spells for damage output and killing. But if you mix it with another skill, it adds a great deal to your options and enhances your abilites.