Tom Kite matched the course record in round two with a 9-under 63. He shares second place with first-round leader Dana Quigley at 11-under-par 133. Lonnie Nielson is one stroke further back at minus-8.
The first round was completed Saturday morning after it was suspended for the night Friday due to lightning and heavy rain.
Weibring began his second round with birdies on each of the first two holes to get to 7 under. He stumbled to a three-putt bogey on four, but got that stroke back with a birdie at the next.
The two-time winner on the Champions Tour faltered to another bogey on the seventh, but moved back to 7 under with a 6-foot birdie putt on the ninth.
Weibring, who will turn 52-years-old on Wednesday, caught fire on the back nine. He converted a 13-foot birdie putt on the 12th and made two straight with a birdie at the 13th on Greystone Golf & Country Club.
He kept rolling with a birdie on 14. Weibring capped a run of four birdies in a row on No. 15 when he sank a 3-foot putt. He moved into the lead outright with an up-and-down birdie at the last.
'I've been off for a few weeks, but I've had a good, solid two days so far,' said Weibring. 'The key for me is that I've driven the ball solidly and putted pretty good too.'
Weibring will have his work cut out for himself on Sunday. Just six of the previous 13 second-round leaders have gone on to win the title here. However, if he does go on to win, Weibring would be the 14th different winner in the events 14 years.
'I'll try to be reasonably aggressive on Sunday,' Weibring said. 'They'll be coming up the board.'
Kite jumped from a tie for 14th to a share of second with his bogey-free round. He opened with three straight birdies to get to 5 under. The Texan carded his fourth birdie on No. 5.
The 55-year-old again birdied three holes in a row from the 11th to get to 9 under. Kite took the lead at minus-11 thanks to birdies on the 15th and 17th. However, he only managed a par at the last to share second place.
'It's been a long time since I've had a round like this,' said Kite. 'It was a great day for scoring.'
Quigley, the tour's ironman, is making his 272nd consecutive start for which he's been eligible and 258th straight overall. He birdied the second and fifth to get to nine under.
The 58-year-old Quigley, who ran off eight birdies in a row in round one, parred nine straight holes from the sixth. He dropped in a birdie putt on the 15th and Quigley two-putted for birdie on the par-5 closing hole to share second place. He has now posted 23 straight rounds of par or better at this event.
Mark James, Curtis Strange and Tom Jenkins, the 2003 champion here, are tied for fifth place at 7-under-par 137.
Bruce Fleisher, the defending champion, leads a group of five players one stroke further back at minus-6. He was joined there by Allen Doyle, Mark Johnson, Wayne Levi and 1997 Bruno's champion Jay Sigel.