I'm about to start raising weaver in earnest, and I remembered that someone linked to something that gave good info about the cross-class abilities that help with crafting, but I can't seem to find it. Does anybody have that, or want to give me a quick rundown of what I should learn from other crafting classes before I dive in completely?
Possibly this:
http://www.reddit.com/r/ffxiv/comments/1mh6um/crafting_guidetheorycrafting_dont_let_crafters/
As a 50 weaver myself I can tell you that Hasty Touch (Culinarian) combined with Steady Hand, Tricks of the Trade (Alchemy), Waste Not (Leatherworking) and Rumination (Carpenter) are all very helpful in being able to consistently HQ 1* greens+. I find myself using them in that order of importance. The only cross class level 15 skills I don't have yet are Blacksmith/Armorer so I can't speak to those.
Hasty Touch combined with Steady Hand I gives you a 70% chance to improve quality at no CP cost, useful for ramping control way up after starting off with Inner Quiet. Tricks of Trade gives you 20 CP on every "Good" condition by turning it to Normal condition, no durability or CP cost on that. Waste Not halves durability cost for 4 turns and has gotten me out of some tight situations. Rumination will let you get a couple more touches in at the end because you know you can get enough CP back to either restore enough durability to finish off the progress or, like I find myself doing most often, getting Waste Not in at the end to finish up on progress.
Some people use Manipulation more but I haven't found myself using it much; on 40 durability mats I just do three Great Strides + Advanced Touch then finish up and that gives me a good enough chance (~70%+ on wool) of a HQ product. I haven't focused on 100%ing the quality on 40 durability items yet since it's rarely worth the extra time of adding another dozen steps to it, and the final product will be HQ regardless.
Good luck!