Weibring completed 36 holes at 13-under 131 to match the 36-hole scoring record Ed Dougherty set in 2000.
Thorpe, who shared the lead after one round with Tom Jenkins, had a 4-under 69 Saturday.
"It was a challenging day out there," Weibring said of the breezy, rainy conditions. "I hit the ball solid today. Whenever you shoot 31 on the back nine, especially in tough conditions, it gives you a good feeling."