Grookey is the stick.
The monkey is just a regular animal that is enslaved to the Grookey the moment it picks it up. Grookey itself is a parasite, think of a sort of fungus.
Despite this, the evolution of Grookey is meant to be so deceptive that the stick literally never changes throughout the evos, it won't get bigger, it won't be used as a weapon. Only the enthralled monkey changes due to the parasitic mind altering effect Grookey has on the monkey , it's for this reason that Grookey's final evo is Grass/Dark, due to the moral implications that come with this.
When the monkey has outlived its usefulness, Grookey will sap its remaining life force before lying in wait for another monkey to pick it up.