Kuchar was at 11-under-par 131 with Tiger Woods just five shots back in a tie for 8th place alongside players including Rory McIlroy and Justin Rose.
2012 U.S. Open champion Webb Simpson and long-hitting Gary Woodland tied for second at nine-under 133 at the halfway mark of the weather-hit tournament.
World number six Kuchar returned with 39 other players to complete the second round and put the event back on track after thunderstorms caused more than six hours of delays on Thursday's opening day.
The 35-year-old Kuchar birdied three of the five holes he had left to play, rolling in a 28-foot putt at the par-three 14th, and bogeyed the two others including the 18th.
Woods, playing in the same group as Kuchar, missed a 13-foot putt for birdie when play resumed at 14 after the suspension due to darkness on Friday, but birdied the 17th to improve to six under par, five shots off the pace.
South African Charl Schwartzel, the 2011 Masters winner, finished up a second-round 67 to reach seven-under 135, a total he shared with reigning Masters champion Adam Scott of Australia, 2011 PGA champion Keegan Bradley, and Rickie Fowler.
Two-times major winner McIlroy returned on Saturday to complete a 65 that featured eight birdies to join a group of nine at 136.
Along with world number one Woods, the group also included U.S. Open champion Rose and fellow Briton David Lynn, Spain's Sergio Garcia, Sweden's Freddie Jacobson and Jonas Blixt, Brandon de Jonge of Zimbabwe and American Jim Furyk.