Level 7 is the cap. You don't have to be a level 7 weaver to make this. It just means that level 7 is the highest level your skill wil rise to by making this item.
the people that give you guild recipes can also give you "support". all the guilds i've been to, there seems to be 3 of them... 2 will give you basic image support for free ("Your skill improves ever so slightly"). the third will give Advanced image support, for the nominal donation of 30 gil. ("Your skill improves a little bit.")
i'm -guessing- that basic support is like .1-.2... and advanced support is maybe like .5 bonus to skill.
It is 30 gil if you're lower than level 10 in your craft. Every 10 levels, the price rises another 30 gil. For instance, my Woodworking is at 35.6, and advanced support now costs me 120 gil. Back when I was in the 20s, it was 90 gil, and so on. Still, it's not that much; even at level 90+, advanced synth support would only cost 300 gil.
You have to make sure you are using -Cotton thread- and not Grass Thread. Otherwise you will be making a difficulty 16 Kenpogi. Wasted so much grass threads and cloths like this. *DOH*
I think the level is wrong on this. I attempted to synth it at level 0 and received a message that my skill was too low. This was with image synthesis support. When I got to level one, I paid 30 gil for the advanced image synthesis support and tried it again. I was allowed to attempt to make it, but I failed three times in a row. I lost my crystal all three times and thread and cloth on two attempts. Seems more like it should be level 5 or so.
The levels they give are not a requirement to make the item; they are the level your skill will cap when making them. This has a level 7 cap, meaning that you can recieve skillups making this until level 7.