The triumph also maintained our 100% record against the Hammers with five from five in all competitions, keeping Gareth Taylor's side in title contention.
There was further cause for celebration, as January recruit Abby Dahlkemper was handed her debut, while Aoife Mannion also celebrated her long-awaited return from injury, making her first appearance since October 2019 following a lengthy spell of absence with an ACL injury.
Having endured a mixed start to the 2020/21 campaign, City found their rhythm in December and ended the first half of the campaign in a rich vein of form - and with a game in hand, the 2016 title winners began to mount a serious challenge for the crown.
Weir, who netted twice in 17 minutes on the south coast last Sunday, needed just nine minutes to break the deadlock this time, bagging her fourth goal in as many games.
Collecting Mackenzie Arnold's goal kick, Lucy Bronze outmuscled Mayumi Pacheco before driving down the flank and finding Chloe Kelly. The winger whipped in a cross, which bounced to the backpost, where Scotland Player of the Year Weir pounced, drilling across to the far corner.
From that moment on, it was one-way traffic. As City pushed for a second, Bronze, Kelly, White and Keira Walsh all went close but it was Stanway who would strike six minutes before the break with her sixth goal in five games against West Ham.
Once again, Bronze was involved, delivering a cross which the Hammers failed to clear. A spell of pinball eventually saw the ball fall to the feet of Stanway who smashed home from close range for her tenth goal of the season.
City continued where we left off after the break. Cross-shots from Kelly and Hemp almost yielded a third - the latter hitting the woodwork - but White would claim the honour, grabbing her seventh goal in 13 league games with a headed flick-on from Alex Greenwood's corner.
Introduced from the bench, Lavelle made her first appearance since mid-December, returning from injury, and made an instant impact, capitalising on a Pacheco mistake and finishing with aplomb for her first WSL goal.