To what end does Chillingworth use the black weed he picks from the cemetery in The Scarlet Letter?
In chapter 10 of The Scarlet Letter Chillingworth and Dimmesdale are together looking for herbs, as the later is actually posing as the physician of the latter. When they come near the cemetery, Chillingworth finds some weeds that are coming out of a location which is described as
... a grave which bore no tombstone, nor other memorial of the dead man, save these ugly weeds that have taken upon themselves to keep him in remembrance
These were presumably weeds born out of a dark secret from the dead man buried underneath, which is a direct pointing to Dimmesdale and the secrets that lurk within his heart, and which keep him ill.
Chillingworth would have made a potion with those herbs had he really intended to do so in the first place. However, his intention was to mortify Dimmesdale and touch upon his suspicion that the Reverend had a dark secret that was killing him from the inside out. As Chillingworth suspects that Dimmesdale and Hester have some sort of connection, he uses the black weeds sort of to taunt him into confessing and to make him feel really bad. Moreover, he uses the weeds from the cemetery to remind Dimmesdale that life is finite, that he is a man of the cloth, and that he owes it to his soul to confess and let his sins be pardoned by a Higher power. To this, Dimmesdale completely rebuffs and says that Chillingworth has no clue about the troubles of the soul, just the body. Conclusively, taunting and mortifying Arthur Dimmesdale is the true end for which Chillingworth really uses the weeds.