With the score tied 2-2 after 5 1/2, Corey Hart smacked a two-run shot to put the Brewers ahead and, four batters later, Weeks belted a 1-2 pitch from Bud Norris (1-1) high over the Milwaukee bullpen in left center field.
Travis Ishikawa added a two-run home run and Carlos Gomez contributed a solo shot for the Brewers, who notched their 11th straight win over the Astros and clinched their three-game series at Miller Park.
Randy Wolf (1-2) collected the victory after yielding a pair of runs on four hits over six innings, overcoming four walks and striking out four.
Norris was roughed up for seven runs on nine hits over a 5 2/3-inning start.
Jose Altuve cracked a solo homer for Houston.