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Weeks, who turns 29 on Jan. 26, has played parts of five seasons at the big league level with the A's, Orioles and Red Sox. He had three hits in nine at-bats with the Red Sox in 2015, spending most of the season at Triple-A Pawtucket, where he hit .204.
Weeks, the 12th overall pick of the A's in 2008, is a second baseman by trade, but he can move around the diamond. His best season was his rookie year with Oakland in '11, when he hit .303/.340/.421 in 437 plate appearances.
Weeks gives the Padres some organizational depth in the infield, as does Rosales, who signed his Minor League deal with the Spring Training invite on Jan. 1.
San Diego will head to Spring Training next month with a projected infield of first baseman Wil Myers, second baseman Cory Spangenberg, third baseman Yangervis Solarte and shortstop Alexei Ramirez.
Ramirez, a free agent, has agreed to a one-year deal. His contract hasn't officially been announced by the team yet.
Jose Pirela, obtained from the Yankees in November, can play second base and the outfield as well. Alexi Amarista, the Opening Day starter at shortstop a year ago, also figures in the infield mix.
Weeks is the younger brother of free-agent infielder and former All-Star Rickie Weeks.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.