The Canadian left-hander, who opened with a sparkling 63 at the Pebble Beach Golf Links, fired a five-under-par 67 at Poppy Hills in surprisingly cold and foggy conditions on the Monterey Peninsula.
That left Weir at 14-under 130, with American Jonathan Byrd alone in second place after returning a 65 at Pebble Beach.
Another American, Mark Wilson, was a further two strokes back in third after a 68 at Pebble Beach while South African Tim Clark was among a group of five at seven under following a 71 at Poppy Hills.
Britain's Luke Donald, one shot ahead overnight after a course record-equalling 62 at Spyglass Hill, was at nine under with four holes to play at Pebble Beach.
Champion Phil Mickelson was at seven under after 14 holes at Spyglass, usually considered the toughest of the three tournament venues.
Weir, who has finished eighth or better in five of his last six appearances in the event, reached the turn in one-under 35 after teeing off at the 10th.
He then picked up his fourth birdie of the day by sinking a 10-foot putt at the par-three second to take the outright lead at 11 under.
After four consecutive pars from the third, the 2003 U.S. Masters champion distanced himself from the chasing pack with his three-birdie finish.
Best early round of the day in the testing conditions was Byrd's eight-birdie 65.
The twice PGA Tour winner birdied the first four holes, faltered briefly with a bogey at the par-three fifth where he found a bunker off the tee and picked up further shots on six, 13, 14 and 16.
"My game is really good right now," Byrd told reporters.
"Every part of it is solid and I'm hitting a lot of greens which helps. Today I finally putted well, too."
Byrd, who won the 2002 Buick Challenge and the 2004 B.C. Open, said the change in conditions from the glorious sunshine of Thursday had been significant.
"At the start of the day, it was really sunny with blue skies but then the fog rolled in," he said.
"It got colder, the ball did not go as far and the biggest change was the greens which were really firm.
"The greens are so small here at Pebble and you just don't want to leave yourself with putts above the hole. I did a good job of that today," added Byrd, who tied for seventh at last week's Phoenix Open.
"I felt if I could shoot five under on each of the three courses, I'd have a chance on Sunday. So I am right on pace."
The field of 180 professionals and 180 amateurs play each of the three venues over the first three days before the leading 60 professionals and ties qualify for Sunday's final round on the Pebble Beach Golf Links.