It took Weir just nine minutes to open City's account after she tapped in a Chloe Kelly cross from close range.
Kelly was on hand again on 39 minutes to feed the ball to Lucy Bronze who struck a cross into the box which Stanway hit home.
White added City's third when she got on the end of an Alex Greenwood corner and headed the ball into the net.
Lavelle, who has just rejoined City after being with the USWNT, sealed the win on 71 minutes when Mayumi Pacheco lost her footing and Lavelle capitalised on the error.
Aoife Mannion made her return to action from an ACL injury suffered in October 2019 when she replaced Weir on 78 minutes.
City have now extended their unbeaten home run to 28 games and have scored 18 goals in their last three games.