The word "divvy" comes from the 19th century American slang term "dividend," meaning a share of something.   It was initially used as a noun to refer to a dividend or a share of something, but later evolved into the verb "to divvy up" (to divide and share), first appearing around 1877. The word's root is the Latin verb dividere, meaning "to divide".  In British slang, "divvy" or "divvie" can mean a stupid or foolish person, similar to "dimwit". It can also be used as a verb meaning to divide or share something, as in "divvy up the profits".  

According to the Oxford English Dictionary (OED), the verb "divvy" was first used in English in the 1870s, with the earliest known evidence dating to 1877 in the writings of L. Grover.  It first appeared in American English as a noun in the mid-1860s, referring to a dividend, with the earliest documented evidence dating to 1872. 

Examples of the word "divvy" used in a sentence: 
 To share resources: "The team agreed to divvy the costs of the new equipment equally." or "The group of friends decided to divvy the cost of the spring break trip." 
To distribute items: "The workers were told to divvy the stolen goods among themselves." or  "The pirates will divvy the stolen treasure amongst themselves." 
To allocate responsibilities: "The manager asked each employee to divvy up the daily tasks." or "The work of analyzing the data was divvied up among the researchers. 
Referring to a share: "We each got a small divvy of the profits."  or "The friends decided to divvy up the pizza slices." 
In British English, it can be used humorously to call someone a foolish or silly person: "You're such a divvy if you think that will work." 

Just the facts:

DIVVY Definition & Meaning - Merriam-Webster

DIVVY (UP) Synonyms: 60 Similar and Opposite Words | Merriam-Webster Thesaurus