Just making the cut is news for Wetterich, who failed to qualify for the weekend in 14 of his first 16 PGA Tour starts, including five this season.
But the 28-year-old Wetterich, who lives an hour away in Palm Beach Gardens, finished a bogey-free 6-under-par 66 Saturday morning before going 4-under through 11 holes of his third round.
Wetterich was one of 50 players left on the course, which was drenched with two inches of rain Thursday, leading to darkness suspending rounds on Friday and Saturday.
Ranked 12th in the world, Weir also completed a 66 early Saturday, then went 3-under over 10 holes of the third round to grab a share of the lead at 14-under heading to Sunday.
PGA Tour rookie Stephen Gangluff, who has missed his first four cuts this season, finished his round at 13-under 203, as did Matt Kuchar. Gangluff carded a third-round 65, one shot better than Kuchar.
Wetterich has never finished better than 63rd in a PGA Tour event and has a medical exemption after undergoing wrist surgery in January 2001.