Weston opened the scoring in the fifth minute against Peterborough Sports with a 25-yard bullet, before Dan Jarvis equalised six minutes later.
Weston netted the winner in the 72nd minute with a neat near post finish following Cameron Green's knockdown.
United: Cameron Gregory, Michael Bostwick (Cameron Green 64), Tom Leak, Keaton Ward, Martin Woods (Jordan Richards 46), Dan Mooney (Frankie Maguire 64), Jai Rowe (Jacob Scott 87), Tony Weston, Pemi Aderoju (Jacob Hazel 57), Zak Mills (Mitch Roberts 46), Dylan Hill. Subs (not used): Adam Marriott, Sam Osborne.
Referee: Minesh Gupta.
Attendance: 353.
PIC: Lee Keuneke.