Webb, who collected four birdies and two bogeys for a 70 at the Royal Pines Resort on Friday, is attempting to win an unprecedented fourth straight Masters title.
Brooky began the day at the 10th and posted three birdies to make the turn at 9-under for the tournament. Although she was able to add four more birdies over the second nine, a missed three-footer for birdie at the sixth kept her from matching her career-best round of 8-under-par.
'I've had rounds this low before, but this is the first time I've put together two rounds like this,' said Brooky, who was one stroke out of the lead after opening with a 66 on Thursday. 'It's a bit scary to be honest. But I know I'm hitting well and have got my swing right so I'm looking forward to the next couple of days.'
Brooky captured the Ladies Austrian Open in 1998.
Robbins also made her way around the par-72 layout without a bogey on Friday, carding five birdies for a second-round 67.
'I'm really pleased, I had no bogeys, I've been playing solid and I'm looking forward to the weekend,' said Robbins, a nine-time winner on the LPGA Tour. 'I probably left a few birdies out there. I think I hit the cup three times on the front side, so I really had to try and
Australian Corinne Dibnah shot a 70 and is currently tied at 6-under 138 with first-round leader Diane Barnard of England, who dropped from the top with a 1-over 73 in Round 2.
England's Laura Davies, the champion of this event in 1993 and '94, turned in rounds of 77-76 to miss the cut by six shots.
This is the season-opening event on the 2001 Evian Ladies European Tour.