Fleece is one of the primary materials for a weaver level 40+. It makes both woolen things (mostly 40-45) and is also necessary in felt things (lvl 45+). Unfortunately, fleece is a pain to come by at the moment. There is one group of sheep in the game who drop it (Ornery Karakul, located below Dragonhead in Coerthas). The drop rate is actually pretty good, but they are currently overfarmed like nobody's business. Competition and mob stealing is fierce out there, and when you have six people camping the same three sheep, things can get heated.
Sometimes you can send a /tell to a person farming an area, to the effect of 'hey, can you let me know when you're done?' and politeness and cooperation will ensue. But mostly you'll be killing sheep and someone will run up and start trying to snipe them from you, because 'they do what they want!'
In any case, this whole thing is a stressful, frightful mess. (Unless you enjoy sniping people's kills and fighting with other players. In that case, go for it.)
For anyone who doesn't find this fun, I present to you alternate methods for obtaining fleece.
When you reach level 40 as a weaver, you're able to do leves in Whitebrim Font in Coerthas. The leve "No country for Old Men" requires you to turn in one pair of woolen tights. Woolen tights cost 10 fleece to craft. The leve will often reward you with 15 fleece. This is a profit of 5 fleece. Similarly, when you reach level 45, you can do the leve "And A Haircut Wouldn't Hurt" in Saint Cornach's Find, Mor Dhona. This requires a turn in of one felt robe. Felt robes require 10 fleece to construct (as well as snurble tufts, natron, and electrum ingots). You can be rewarded with 16 fleece though.
The trick of all this is that the leves don't ALWAYS reward you with fleece. Sometimes they reward you with shards, and other times with moldering hats and items you can craft into vintage gear. As far as I know, the leve rewards randomly reset every time you turn one in to that person. However, this method will at very least offset the amount of fleece you need to either gather or buy while leveling your craft.
Another method I have found for leveling weaver is to simply do the level 35 quests, and try to HQ them. In the Sanctum Aetherial Astrological Phenomena (also in Coerthas), there is a level 35 quest entitled "A leg up in the cold." This one wants a turn in of 3 linen tights. Since flax (used for linen) is a botany item, it's much easier to come by (and cheaper.) For a bonus, the leve sometimes gives Flax back, AND it's one of the leves that will allow you three chances to turn stuff in. So, you can have three times the amount of experience and (potentially flax) back for one leve allowance. I've found that it's still viable as a leveling method, even in the high 40s, especially if you can manage a full 3 HQ tights turn in. (And even if you can't.)
This is old news for some of you I'm sure, but I figured I would post it for those who weren't aware. If anyone has found any other good methods for leveling weaver, feel free to let me know! Good luck guys!