Deep into injury time, after a plethora of chances, Weir curled in a long-range effort to seal victory for City at the Academy Stadium.
Weir, who had a hat-trick of assists last weekend, was thrilled with how her team performed in against their top-four rivals.
Its huge, Weir said. We knew we needed the three points, just with the league standings at the moment and were delighted. Thats the third good result this week so were really happy with that.
Arsenal started the better of the two sides and went ahead in the third minute when Vivianne Miedema fired home from the edge of the area.
City had their chances through Sam Mewis who had shots wide and over the bar, but Gareth Taylors side equalised from a set-piece with half an hour on the clock.
Chloe Kellys corner found the US international in the box and she headed home her third goal of the season to put the sides level.