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.
What it means
City remain in third place with 27 points from our opening 12 games, savouring another goal difference-boosting triumph.
Taylor's side sit five points behind table-topping Chelsea and second-placed Manchester United with a game in hand over the Reds.
West Ham stay tenth - level on points with Aston Villa - and two points above Bristol City.
How we lined up...
Taylor made just one change to the side which celebrated our seven-year anniversary with a 7-1 win over Brighton last time out, handing Dahlkemper an immediate debut in place of Esme Morgan.
Walsh protected the back four, employed behind Weir and Stanway with Kelly and Hemp occupying the wings. White led the line upfront.
CITY XI | Roebuck, Bronze (Coombs 64'), Houghton (C), Dahlkemper, Greenwood, Walsh, Weir (Mannion 76'), Stanway, Kelly (Davies 84'), Hemp (Lavelle 64'), White.
SUBS | Bardsley, Window.
WEST HAM XI | Arnold, Redisch, Flaherty (C), Fisk, Vetterlein, Pacheco, Longhurst, Joel (Barker 71'), Van Egmond, Svitkova (Cissoko 81'), Leon (Nor 85').
SUBS | Brosnan, Dali, Thomas.
Player of the Match: Alex Greenwood
Solid at the back, Greenwood helped City to another clean sheet - but it was her attacking prowess that impressed on Sunday.
The left-back caused havoc with her deadly deliveries - one delightful cross providing the assist for White's goal.
A composed display all round.
• City have won all four of our Barclays FA Women’s Super League matches against West Ham, scoring 19 goals and conceding only twice.
• Taylor's side are currently on a run of 28 home league games without defeat (W23 D5) - already nine games longer than the next best such run in the competition’s history (Arsenal, 18).
• The four-goal haul means City are the league's top goalscorers this term, having tallied 18 goals in our last three league games.
City have a week's break before travelling to Arsenal in another crunch FA WSL clash.
Taylor's side face the Gunners on Sunday 7 February in a 14:30 (UK) kick-off at Borehamwood with the game set to be broadcast live on BT Sport.
Match highlights from Sunday's game and a full 90-minute replay of the match (available with a CITY+ subscription) will be available from noon UK time on Monday 1 February.
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