He first appears as a fake environmental auditor who forces Bogdan Wolynetz to sell his car wash to the Whites by having Skyler White feed him lines through an ear-piece during his meeting with him ("Open House").
Kuby appears again when he and Huell confront Ted Beneke at his house in order to force him into signing a check to the I.R.S. to prevent Skyler from being audited, as she previously helped him defraud the federal government and can't afford the backlash while she's operating Walter White's illegal front company (the Car Wash).
After intimidating Ted into signing the check, he explains that he'll mail the check and then keep him hostage for a few days until the check clears. But Kuby and Huell are surprised when Ted makes a sudden sprint for the door to escape, trips on an area rug and crashes head-first into the kitchen island, breaking his neck. Kuby and Huell believe Ted dead, and flee the scene.
Kuby and Huell report to Saul's office, explaining what happened as an "act of God," and confirming that they at least mailed the check. Moments later Walter bursts into the office and – assuming he's heard about the incident with Ted – they try to hold him back. Saul realizes that Walter has no idea and then tells them to leave. ("Crawl Space")
Skyler visits Ted in hospital, where he is recovering from his broken neck. He pledges to say nothing to the authorities about Skyler, Kuby or Huell out of fear for his family. ("Live Free or Die")
Later, Kuby helps Walter White, Jesse Pinkman, and Mike Ehrmantraut stop a train in the desert in order to steal from it 1,000 gallons of methylamine. While pretending that his truck has broken down the tracks and halting the train, Kuby asks the engineers to help start his truck back up again. Simultaneously, Walt, Jesse, and Todd begin siphoning methylamine and putting water back into the train, so that no change of weight would be detected. Kuby is able to keep the train engineers distracted for as long as he can before a "Good Samaritan" in another vehicle arrives on the scene, offering to help push the truck out of the way. The man pushes Kuby's truck off the tracks and clears the train's way, then offers to give Kuby a ride into town. Knowing he can stall no longer, he accepts. ("Dead Freight").
After Hank discovers Walt's true identity, Walt has Saul send Kuby and Huell to the storage unit in which Walt has stored his millions of dollars in drug profits. Kuby and Huell can't resist channeling Scrooge McDuck and lie down on the pile of cash. On the money pile, Huell suggests "Mexico," but Kuby points out that Walt had ten men killed in prison within a two-minute window. Kuby and Huell then pile the money into barrels, which they put in a van (a Chevrolet Express). Behind Saul's office, they hand the van over to Walt ("Buried").
Kuby meets with Saul and Walt to report on his attempt to locate Jesse after the latter's aborted attempt to burn down the White Residence. Kuby tells them he has had no luck, and he's been spying on Badger and Skinny Pete, mentioning that they talked for 3 hours about "something called 'Babylon 5'". ("Rabid Dog")
Kuby's ultimate fate is unknown. While Hank, in an effort to frighten him into revealing information, does posit to Huell that Walt has had Kuby killed as a loose end, Saul's former henchman is then never mentioned again.