Hoch, who turned 50 last year but has battled left wrist problems since surgery in late 2005, finished the event with a 15-under 201 total at The Hills Country Club. He earned $240,000.
Weibring finished with a 67, and at 13 under for the tournament. It was his best finish since a win at the 2005 Bruno's Memorial Classic.
'This is very satisfying. I hung on to win, but it feels good,' Hoch said. 'They certainly didn't make it easy on me today, but it always feels good to win when you've been tested.'
He held a three-shot lead over Weibring going into the final day and never trailed or was tied on the last 18 holes, holding at least a two-shot lead for the last 11 holes.
Loren Roberts shot 66 to finish third with a three-day total of 204. Hale Irwin shot 70 to finish fourth at 207 on the Jack Nicklaus-designed course just outside Austin.
'I played good and putted great today,' Roberts said. 'It was a lot of fun.'
Hoch birdied holes three, six and eight, then had his first bogey of the tournament on the par-4 ninth.
After four straight pars to open the back nine, he birdied holes 14-15 to open a three-shot lead over Weibring. His last scary moment came when his tee shot on the par-3 16th barely cleared the water, and that allowed him to finish with three straight pars.
'I felt calm hitting the ball today and didn't make many iffy swings,' he said.
Weibring called it a frustrating final day. He made birdies on holes 3-6 along with 14 and 16, but never could close the gap on Hoch.
'I played well, but Scott just played very well. I had some chances early, but could never close the deficit,' he said.
Local favorite Tom Kite, looking to break an 0-for-107 streak in home-state tournaments, got off to a hot start with birdies on three of the first six holes, but could not sustain the momentum. He finished at 8-under for the tournament and 67 for his final round, alone in fifth place.
His highlights including putting in from off the green for a birdie on the par-3 16th, which brought a first pump from Kite, and a birdie on the par-5 18th.
'It's going to happen. I feel it and it's going to be fun,' Kite said of a victory in Texas.