Both of Weekley's previous wins had been at Harbour Town, in 2007 and 2008.
Almost as quickly, their one-stroke deficit was back to two after Weekley's birdie at No. 13.
Weekley had just made an 18-foot birdie at No. 9 to get to 12 under.
"It feels good to actually have butterflies again, knowing that I'm in this, an opportunity to maybe win, " Weekley said.
While on the easy par-5, 548-yard first hole, the long-hitting Weekley told his caddie that it was good to feel butterflies again.
Australian friends Stuart Appleby and Robert Allenby are also paired together, as are Boo Weekley and Bubba Watson, former high school team-mates.
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Kuchar punched his right arm into the air to punctuate the shot that got him within a stroke of Weekley for the lead.
Weekley hit his birdie putt from about 22 feet, then swiped his putter in the air as if guiding the ball into the cup.
Kenny Perry, Boo Weekley, JB Holmes, Ben Curtis and Chad Campbell were the other American victors, while debutant Hunter Mahan halved with Paul Casey.
Weekley's 22-foot eagle chance at No. 1 stopped about 6 inches from the cup before he chipped in for another birdie from behind the third green.
"I couldn't tell you, it's been so long, " said Weekley, who moved up to No. 55 in the world ranking, making him eligible for the U.S. Open.
Weekley's won the same week he went to see a doctor about the problem he has had recently maintaining focus in his left eye, sometimes causing bad twitches and making it problematic reading greens.
Also at 11 under was American Kris Blanks, with countrymen Jeff Overton and Boo Weekley 10 under and US Ryder cup captain Corey Pavin at nine under alongside Swede Carl Pettersson, former Masters champion Zach Johnson and John Mallinger.
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