The Irons brought Randolph back to East London last month after selling him to Middlesbrough in 2017.
West Ham paid the penalty for not having a quality second-choice goalkeeper in their ranks earlier in the season when Lukasz Fabianski was out injured.
Roberto, who joined the Hammers last summer, originally replaced the injured Pole, but the 33-year-old made a series of calamitous errors during his eight Premier League games under Manuel Pellegrini.
David Martin, who started the season as United's third-choice option, eventually displaced the Spaniard.
And Weaver, who made over 150 league appearances for Manchester City, says that Roberto is potentially the worst senior goalkeeper that he's seen in England's top flight.
"I always have sympathy when goalkeepers get flack. I felt for him but no disrespect to him but he's probably the worst [goalkeeper] I've seen in the Premier League," he told Sky Sports' Football Social.
"I don't want to have a pop at him but he just wasn't up for the job. It's so important to have a reliable number two. Randolph's come in. They know him. He's a safe pair of hands."
Newly-appointed boss David Moyes axed the former Espanyol stopper and sent him on loan to Deportivo Alaves in Spain, after Randolph was signed.
Signing Roberto was one of several questionable transfers that Pellegrini and ex-Director of Football Mario Husillos made last summer, with a £45 million move for striker Sebastien Haller - who has scored six times in 24 league outings - perhaps the biggest of them all.
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