Former U.S. Amateur Champion Jeff Quinney carded a 7-under 65 and Australian Nick Flanagan fired an 8-under 64 to join Weekley in the lead at 20-under-par 196 at Highland Springs Country Club.
The 20-under-par 196 number marks a new 54-hole tournament record, topping Patrick Sheehan's old record of 197, which he set in 2002.
Ken Duke held the lead by himself at 21-under thanks to six birdies through 11 holes, but bogeys at 13 and 18 dropped him down the leaderboard. He shot a 4-under 68 and is tied for fourth place with Doug LaBelle II, who carded a 67 on Saturday, at minus-19.
Weekley played steady golf on Saturday with a 25-foot birdie putt at the second, a chip-in birdie at the fifth and another birdie at the ninth hole.
He tallied a birdie at 12, then dropped his first shot since the second hole of the second round with a bogey at 16. Weekley rebounded from the dropped shot with a birdie at 17 to grab his share of the 54-hole lead.
'It had its highs and it had its lows,' said Weekley, referring to his round on Saturday. 'I hit some good shots, but couldn't make any putts. It's not that I played all that bad, but I didn't play all that good either.'
Quinney, who won the Amateur in 2000, flew out of the gate on Saturday with an eagle at the first. He bogeyed two, but birdied the third to reach 15 under par for the championship.
He collected four birdies in a five-hole span around the turn, then birdied the last to get in at minus-20.
Quinney lost a playoff last week at the Scholarship American Showdown at Somerby, but has a plan for Sunday.
'I just want to go out there tomorrow and go as low as I can,' said Quinney, who won the 2004 Oregon Classic. 'I've got to shoot 7 or 8 under to have a chance to win. I've been in this situation the past couple of weeks so hopefully that will help.'
Flanagan made his move up the leaderboard with a tournament-record-tying seven consecutive birdies from the second. He birdied the par-3 15th to get into first place.
'I holed my fair share of putts,' said Flanagan, who hit 17 of 18 greens on Saturday. 'I pretty much holed everything that I looked at. It was one of those things where you just get on a roll.'
Jaco Van Zyl (63), Justin Bolli (66) and Ricky Barnes (69) are knotted in sixth place at 18-under-par 198.
Stephen Marino posted a 7-under 65 on Saturday and is alone in ninth place at minus-17. Ryan Armour (63) and Jess Daley (66) are tied for 10th place at 16-under-par 200.