Weeds can be gather by hand or with a hoe from any plants (herbs, fruit trees, vegetables, mushrooms, bushes etc).
50 weed can be combined by drying into a Hay Stack.
Weeds can be replaced with Wild Grass in Alchemy and vice versa.
Alustin in Velia offers a Trace of Earth in exchange for 200 weeds and General Goods Merchant Lara in Heidel exchanges them for Gathering XP (100 weeds), Crafting Material (200 weeds, this will yield a Trace of Origin) or Contribution Point XP (300 weeds).