As revealed in the Season 1 episode "Close Rick-counters of the Rick Kind," the reason Rick keeps Morty around as a sidekick is not because he is helpful in any way, but because Morty's brainwaves naturally act as a camouflage for Rick. Essentially, this means Morty is so dumb that he is able to counter-balance the brainwaves made from Rick's hyper-intelligence.
According to a theory from Redditor u/eskadaaaaa, Jerry's role in the story is similar to Morty's — except his brain waves are meant to conceal Beth's instead. Beth Sanchez is Morty's mother and Ricks's daughter, and she has proven more than once to be just as much of a genius as he is. The general consensus in the show is that she's only stuck with Jerry because he got her pregnant in high school.
However, according to this theory, Jerry's role in Beth's life is no accident. "Most Rick's set up their Beths with Jerrys because his stupidity serves to hide Beth's potential genius in the same way Morty does for him," the Redditor noted. "Rick intended for Jerry to be camouflage while he wasn't around to protect [Beth], but I don't think he expected them to want Jerry around still when he came back."
The theory would not only explain why Jerry is present in almost every universe we've come across in the series so far, but it would also explain why Rick's loathing of Jerry never seems to go away — because he was never meant to be permanent.