Spawn area is along the south and southeast shores of Kithicor Island; a good spot is the little island off east shore ( -156, 45, 483 ) /waypoint -156, 45, 483 although others report that the coast just before the island is better. Working south and east from the Keep along the high ground above by the water on the east coast has regular spawns.
The weeds are trackable, fast respawning, grass looking non house item that stack. Others report that the respawn rate is not fast enough to justify waiting. It is faster to continue to look for them.
Although excess spiteweed was removed at the end of the earlier quest in the main quest line, when on this quest, the excess does not disappear. So you can stock up for future weeklies.