Riegger, still looking for his first top 10 finish in five full seasons on the PGA Tour, was 12-under.
Weir made eight birdies and a bogey, tying Peter Lonard, John Senden and Lee Porter with the low score of the round.
Paul Casey, Rod Pampling, Danny Ellis and Brett Wetterich were 10-under, while 27 others were within five shots of the lead as the third round began Saturday afternoon.
Defending champion Jesper Parnevik, 17-year-old Ty Tryon and Southern sensation Boo Weekley missed the cut, which tied the tournament record at 4 under 140.
The third round was to begin at 2 p.m. EST, with three-man groups going off the front and back nines. The leaders were scheduled to tee off around 4 p.m., meaning the third round will not be completed before dark.
Nonetheless, the final round should be completed Sunday, tournament officials said.
More than two inches of rain fell on the TPC at Heron Bay on Thursday, leaving dozens of players with more than 18 holes to play Friday and Saturday. The weather also left the course with soft greens that yielded several low scores.
Riegger broke the course record with a 9-under 63 in the rain-delayed first round, then added a 69 in the second Friday to take a two-stroke lead over Paul Casey.
``I'm playing well right now,'' said Riegger, winless in 115 tour events. ``I'm going to go out and try to continue to do the things I've been doing. They seem to be working pretty good right now.''
Riegger made 12 birdies, three bogeys and an eagle in 33 holes Friday. He had a chance to tie the tournament record of 62 in the first round but just missed a birdie putt on his final hole, the par-5 ninth.
``I knew I was playing well, I was holing some putts, but I wasn't thinking any particular number,'' said Riegger, in his fifth full season on tour. ``Once I got it going, I was just trying to birdie every hole.''
Riegger's best tour finish was 12th in the 1993 St. Jude Classic.
``Unlike a lot of players, I have problems early in the tournament,'' Riegger said. ``If I get myself in a position to do well, I usually do all right.''
He attributed his two strong rounds to a new preshot ritual.
The 38-year-old golfer from Las Vegas repeats a few phrases to himself as he prepares for every shot. Not wanting to disclose the exact language, he says they are words of encouragement that help him stay focused.
He began the routine two weeks ago after working with a sports psychologist, and it started to pay off Friday.
``It's just early in the tournament I have a hard time focusing,'' he said. ``That's pretty much what I'm working on.''
Joey Sindelar, looking for his first PGA Tour win since 1990, did not make a bogey in the first two rounds and was among seven golfers at 9 under.
``I'm having feelings of a time warp here,'' said Sindelar, the 1988 Honda Classic champion. ``How many decades has it been since I've been at a Honda Classic press interview? It's been a while.''
News, Notes and Numbers
*The Honda Classic was officially moved Saturday. Next year, it will be played at a new Arthur Hills course in Mirasol, a planned community in nearby Palm Beach Gardens. In 2004, it will move to a Tom Fazio course in the same development.
*Steve Flesch recorded the fifth hole-in-one in tournament history when he aced the 186-yard par-3 with a 5-iron. He was 3 under after the second round.
*Craig Barlow, who shot 2-over in the first round, withdrew before the second round.
Full-field scores from the Honda Classic