The Scottish international got the goal that her performance deserved when she opened up her body and curled home from the edge of the box for her first WSL strike of the season.
Vivianne Miedema had put the visitors ahead within three minutes with a typically clinical finish before Sam Mewis’ second goal in the space of four days hauled us level just after the half hour.
But it was Weir who made the decisive contribution with her dramatic stoppage time winner, hauling Gareth Taylor’s side to within a single point of the WSL top three.
While both sides were prepared for battle from the off, they united under a common cause in the build-up to proceedings in honour of Arsenal defender, Jen Beattie.
The former City centre-back went public about her breast cancer diagnosis on Saturday and, as a show of support, both sides sported her name and number during the warm ups.
Once the game began, it was the visitors who certainly started the brighter, and they took a deserved lead inside three minutes.
Miedema pounced on a loose pass on the edge of the box before the WSL top scorer curled a typically clinical finish into the far corner past the despairing dive of Ellie Roebuck.
But City weren’t phased by that early setback and were immediately searching for a way back into the game, with Mewis flashing an effort wide from the edge of the box four minutes later.
The American was again in the thick of the action ten minutes later, floating a terrific ball over the Arsenal defence into the path of the onrushing Weir, but she couldn’t keep her volley down under the attentions of Beattie.
And Mewis' standout first half display was rewarded when she got on the end of Chloe Kelly’s corner in front of her marker to head home through a crowd of bodies in the 30th minute.
But Arsenal were quick to show that their bright start was far from a mere flash in the pan, with Beth Mead's tantalising ball across the face of the City defence just before the break, inches away from Miedema at the back post.
City’s high press continued to put Joe Montemurro’s side under pressure, with Georgia Stanway’s tenacity almost presenting her with a clear route to goal inside the opening ten minutes of the second half.
Our forward dispossessed Leah Williamson inside the box but, at the crucial moment, lost her footing as she stretched for the loose ball on an afternoon where the Manchester rain was in full force.
And she almost found some joy immediately from out wide when she latched on to a clever reverse pass from Weir, but her effort on goal was blocked.
Weir continued to dictate play from the centre of the park, and almost put us ahead in spectacular fashion in the 67th minute.
A misguided pass from Lydia Williams landed at the Scottish international’s feet from almost 40 yards, but her inventive chipped effort dropped agonisingly wide of the post, much to the relief of the rapidly retreating Arsenal stopper.
And Williams was thankful for the timely interception of Steph Catley ten minutes later which prevented Stanway from surely putting City ahead at the near post from Mewis’ searching ball.
With the game in its dying embers, Steph Houghton thought she had grabbed a last-gasp winner from a corner, but a combination of Jordan Nobbs and Katie McCabe did just enough to prevent our skipper from tapping home at the back post.
But when it seemed for all the world like City would be reflecting on a frustrating draw, Weir stepped up at the decisive moment.
The midfielder reacted quickest to a deflected Stanway drive before bending the ball exquisitely into the far corner.
The late winner was just rewards for a dominant and impressive display from Gareth Taylor's side, who will go into Wednesday's Champions League Last 32 second leg clash with Gothenburg brimming with confidence.
What it means
We remain fourth in the WSL, but the win moves City to within a point of the top three, and just five points from the summit.
How we lined up
Keira Walsh sat in front, allowing Weir and Mewis to get forward in the midfield three.
Hemp and Kelly started on the flanks, with Stanway leading the line.
It's another quick turnaround for City, with Swedish outfit Gothenburg travelling to the Academy Stadium on Wednesday for the second leg of our Champions League Last 32 clash.
Gareth Taylor's side are then back in WSL action four days later, with a trip to seventh placed Birmingham next on the agenda.