Mickelson shot 68-66. He won his PGA Tour Champions debut at the Ozarks National in August.
Weir won the 2003 Masters for the bulk of his eight PGA Tour titles.
His compatriot major champion Retief Goosen finished third at 8 under with Brandt Jobe. They each shot 68-68.
Bernhard Langer, the first round leader after a 67, had 7 under with Wes Short Jr. (69-68) after a second round of 70.
Ernie Els, the 50-year-old former major champion who just picked up his second win of the season last week in North Carolina, shot 72-66 to go down to 6 under.
Jim Furyk, another 50-year-old former major champion who won his first two senior starts, had five cents after rounds of 71 and 68 alongside Mickelson and defending champion Miguel Angel Jiménez.
Jiménez had 1 penny, shooting 74-69.