The Blades have won just one of their 10 league fixtures this term, with that coming on the opening day, and currently sit third from bottom in the table with just five points.
Former Scotland and Everton defender Weir, 43, was only appointed in June, taking up his first job in management.
But his stay at Bramall Lane has not lasted long having been relieved of his duties along with assistant boss Lee Carsley.
Source: PA
Source: PA