Weibring shot a 7-under 63, one stroke off the course record, which was matched Friday by Jim Colbert. Colbert, whose 62 was the lowest second-round score in Senior British Open history, moved to 6-under-par 134 and shares sixth place with Russell Weir.
Mason began the round one stroke behind Tom Kite and Tom Watson, the overnight co-leaders. He opened with a steady front nine and birdied the par-4 third to get his bogey-free round going.
The Englishman two-putted for birdie at No. 7 to head to the back side at 5-under.
Around the turn, Mason sank a three-foot birdie putt at the 10th and followed that with another birdie at the 12th. It was Mason's strong play down the stretch that allowed him to take the outright lead.
Mason dropped a 9-iron within 12 feet to setup up birdie on the 16th. He followed that with a two-putt birdie at the next. Mason parred the last to maintain the 36-hole lead.
'I played delightful. It was pretty nearly flawless golf,' said Mason, who has gone 32 holes without a bogey. 'The only time I was under pressure all day was on the first. But after that, it was stress-free. I never had to hole a tough putt. If I missed a putt, it always went stiff, so it was a real stress-free round.'
Mason enjoyed his pairing the first two days. He played with Jack Nicklaus and Tom Watson during the first two rounds, and their history rubbed off.
'It just felt so good,' said Mason of his pairing. 'They were very quick to say 'good shot.' Afterwards, Jack said, 'I felt like a hacker out there.' I would say it was probably one of the most solid rounds of golf I had ever played, and in the company I was in, that was the best.'
Weibring got started with back-to-back birdies from the fourth to get his round rolling. He followed that with a two-putt birdie at the short par-5 seventh.
He converted four straight pars around the turn on the Ailsa Course at the Westin Turnberry Resort. Weibring then caught fire down the stretch.
He dropped a 9-iron within four feet to setup birdie at the 12th. Weibring, a five-time winner on the PGA Tour, knocked a pitching-wedge to 12 feet at the next for another birdie. He made it three straight with a two-putt birdie at the 14th.
Weibring continued his roll with a five-foot birdie at the 16th and made a strong up-and-down from a greenside bunker for birdie on 17. He could have matched Colbert's 62, but he bogeyed the last hole after his drive found heavy rough. Despite the bogey, Weibring still posted a career-best round.
'I played well through the turn and coming home both days and feel good about that,' Weibring said. 'I didn't like the bogey at the last, but it was a good opportunity to score today. Golf course played very nicely.'
Weibring, who last won at the 1996 Greater Hartford Open, has had a light schedule over the past few years. He is attempting to wipe away the rust from the layoff, as he has appeared in just four events this season, one of them being on the PGA Tour.
'I played Hilton Head this year and made the cut and played okay,' said Weibring. 'So coming in, turning 50, I felt I was prepared, I was in good condition, but maybe not as experienced. I had a little rust in my game. I played that way a little bit.'
Bruce Summerhays fired a 5-under 65 to join Watson and Kite at 7-under-par 133. Weir and Colbert share sixth place behind that trio and Denis Durnian is alone in eighth at 5-under-par 135.
Defending champion Noboru Sugai stumbled to a 3-over 73. He dropped to even-par 140.
The cut line fell at 4-over-par 144, the lowest in event history. A total of 77 golfers, including one amateur, will play the final two rounds. Among those who missed the cut were Steve Veriato (145), Jose Maria Canizares (146) and Dale Douglass (147).