I din't do a single Leve, and yesterday I got my brand-new Weaver to 17 by making one of every item in the Crafting Log. You get an XP bonus the first time that you make an item.

Also, since we have to make a boatload of yarn/thread and cloth, I bumped up a level just grinding away on that stuff. One level for Undyed Hempen Cloth and another level for Undyed Cotton Cloth. Boring? Heck yeah! But you have to do it, so why not get it out of the way right away?

Aside: Because I don't have enough gil to buy materials, I trained as a Botanist and collected all of the Moko Grass and Cotton Boll needed to be able to grind thread and cloth. It looks to me like you need to have 400 Moko Grass and 400 Cotton Boll to be situated to craft each item in your Crafting Log that calls for those materials. To collect 400 items takes about two hours of steady harvesting, <heavy sigh>.