Watney's 36-hole total is 135, one-shot better than Ryan Palmer (65) and John Senden (70).
At 8-under 136, Palmer and Senden are tied for second at the halfway point.
"I started off swinging well and had a few more opportunities early, but then didn't hit it as well as I did yesterday so I made a lot of good par saves," said Watney, who was involved in a three-way tie for the lead after Thursday's first round. "It's tough to get the ball close because the wind was kind of gusting and pretty tricky."
Six players are tied for fourth at 7-under 137.