Ellen White, Gemma Bonner and Janine Beckie all found the net – but it was the Scottish international claiming the assist for each of the goals.
In the opening stages, the game was reasonably even, with Demi Stokes going close for City and Ingrid Moe Wold firing a deflected effort wide.
The Blues went ahead just before the half-hour, with White heading home Weir's well-placed cross.
One minute later, it was Weir's corner that met the head of Bonner at the back post as City doubled their lead.
Beckie should have made it three but put her one-on-one with Sandy MacIver wide – then made up for her earlier error in first-half injury time when she nodded yet another Weir cross in at the far post.
The Toffees had some chances in the second half as Nico Sorenson and Chantelle Boye-Hlorkah both aimed shots on target, and Hayley Raso will be ruing her poor touch in front of goal.