Members of The Woven faction are devoted to a mysterious being known as The Weaver. Not much of her is known, other than her goal to weave a new, perfect world.
The Faction can be joined by talking to Masque inside the Haven of Silk after the completion of a Cemetery of the Erased. You can further improve your rank by earning and spending Memory Amber, which is most commonly found inside Tombs and Cemeteries of the Erased, or by slaying the Weaver's creations.
Echoes containing a Tomb or a Cemetery will always have Silken Cocoons. These destructible objects are found inside and around the entrances to Tombs and Cemeteries. The cocoons can be smashed open to either release a Soul of the Erased, which will empower a nearby enemy, or instead release an enemy trapped inside.
Ranks within the Weaver Faction provide two things; Points to spend in the Weaver Tree, and the ability to purchase new Woven Echoes from Masque. Spending points in the Weaver Tree allows players to tailor their preferred rewards and content inside the Monolith of Fate.