Kuchar was among the 78 players who had to complete their opening rounds early on Friday morning but then got the benefit of going straight back out to play their second rounds before the wind picked up late in the afternoon.
"This is certainly a great place to be," Kuchar said. "I'm looking forward to the opportunity to really do something great this weekend."
Kuchar's previous best finish at a major was when he tied for sixth at this year's US Open.
Britain's Simon Khan briefly joined Kuchar at eight under but bogeyed the last three holes to slip back to a tie for third and leave Watney as Kuchar's closest challenger.
"The course really showed teeth today," Khan said.
South Africa's Ernie Els also had trouble at the end of his round, finishing with a double bogey to end on two under.
"It's not how you want to finish. It was a difficult day," Els said. "I scrambled quite well here and there but just let it go at the end there."
US Masters champion Phil Mickelson had an up and down day, struggling to find the fairway, but holed some long putts for a 69 to join Els at two under.
"I just want to be in a position where if I play like I know I can, I can make up some ground," he said. "And I feel like I'm within striking distance."
Woods, who shot 71 on the opening day, made a solid start to his second round, scrambling to par his first six holes to remain at one under when play was suspended because of fading light.
"It was tough out there, blowing pretty good, had to be very patient," Woods said. "I had to hang in there and did a good job with that. Unfortunately I missed a short one [putt] there at the last one I played but other than that, it was all right."
American Jason Dufner shot a superb 66, the lowest completed round of the championship, to join Bryce Molder (67), Dustin Johnson (68), Zach Johnson (70), McIlroy, Khan and Noh at five-under.
McIlroy had an adventurous day, playing one brilliant recovery shot from the water's edge, and holding his nerve in the tricky conditions to put himself in contention to challenge for his first major title.
"I feel as if I'm in a really good position going into the weekend and I like the position I'm in," the Northern Irishman said.
"Only three behind at the minute. We'll see how the guys in the afternoon make out, but I feel as if I'm in a strong position and a position where I can make a charge for the weekend."