Weeks' solo shot in the first inning put the Brewers ahead to stay and Aramis Ramirez also went deep as Milwaukee clinched its three-game series.
Norichika Aoki, Jean Segura and Taylor Green added RBI for the Brewers.
Estrada (3-6) scattered four hits, issued one walk and fanned six as Milwaukee won its eighth straight home game and improved to .500 (71-71) for the first time since April 24.
Tim Hudson (14-6) absorbed the loss, surrendering four runs on seven hits over 6 2/3 frames for the National League wild card-leading Braves.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes