Simpson, in his second start since claiming the U.S. Open title in San Francisco, moved to 9-under-par 131 at the midway point of a tournament that saw both Tiger Woods and Phil Mickelson miss the 36-hole cut.
Jonathan Byrd, Jeff Maggert, Jerry Kelly and rookie Charlie Beljan shared second place at 132. Beljan, who has survived the cut in just four of his 12 PGA Tour appearances, had the low round of the tournament with a 62.
A dozen players were unable to complete play Friday due to a lengthy weather delay in the afternoon. The only one among them who had a chance to impact the top of the leaderboard was Martin Flores, who was at 8-under with two holes to play.
J.B. Holmes and Charlie Wi both finished at 7-under 133. John Daly shot a 67 and, at 135, survived the cut in his third consecutive appearance on the PGA Tour. First-round leader Vijay Singh slumped to a 74 and was tied for 36th at 137.
The cut came at 139 and Woods finished at 140. It was his second missed cut of the year and came one week after he became the first player this season to win three times on the tour.
Mickelson was a shot behind Woods at 142.