The 23-year-old midfielder featured 39 times for the Mariners last season.
He returns to 1874 Northwich for his third spell after initially joining the club in 2018, graduating from the U21s into the first team.
Weir, who is the son of former Everton defender David Weir, has also featured for the US-based Purple Aces during the 2019/20 season.
Photo credit: 1874 Northwich
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