Great Doddington were unable to convert a number of early chances and the game was goalless at half time.
But Doddington struck early in the second with close-range goals from Stefan Lewis and Lewis Kain.
A further neat finish from Kyle Awbery extended the lead before Weekley hit a late consolation through Lewis Vyse.
Great Doddington: Kyle Awbery, Delroy Codrington, Jamal Conteh, Dawid Jura, Lewis Kain, Stefan Lewis, Edward Luck, Matthew McCarthy, Cameron Mortimer, George Roche, Daniel Uche, Jack Waterman, Jake Westcott, Alex Wills. Great Doddington Greens player of the match: Delroy Codrington.
Weekley Rovers Milan: Taylor Barnes, Liam Berwick, Marco Geranio, Henry Griffiths, Jordan Harding, Sean King, Daniel Landy, Harry Lloyd, Niall Murror, Ben Newman, Brady O’Hagan, Dylan Panter, Matthew Phillips, Jack Seymour, Lewis Vyse. Weekley Rovers Milan player of the match: Niall Murror.