Korea's K.J. Choi, a two-time winner on the PGA Tour in 2002, teamed with S.K. Ho for a round of 11-under 61. They were joined by the French squad of Thomas Levet and Raphael Jacquelin in a tie for third.
Phil Mickelson and David Toms, who partnered for the United States at the Ryder Cup, collected four birdies over the first nine holes.
Mickelson two-putted for birdie at the 10th and the pair added another birdie at the 11th. At the par-4 13th, Toms landed his second shot inside two feet to reach 7-under. The Americans parred the remaining holes to finish six shots off the lead after a round of 65.
Weir and Leggatt were part of a three-way tie for the lead after the first round of this event last year. The pair finished the tournament four shots behind the eventual champions, but at Vista Vallarta Golf Club both players like their chances.
'I think we are both very capable players,' said Leggatt. 'Maybe it's surprising that the country of Canada might be winning the World Golf Championship in December, but I think that's about it.'
The duo made the turn at 5-under in the better ball format. At the par-5 10th, Weir hit his second shot to 15 feet and drained the putt for an eagle.
'A few times we had it in there close and the guy that was outside would make the putt,' said Leggatt. 'That's just how best ball works, it just kind of frees you up a little bit and we did a lot of that today.'
They birdied the next two holes and made it three in a row after Weir ran home a putt from the fringe for a birdie at the 13th.
Weir, who had a quiet year on the PGA Tour in 2002, was on top of his game at the Nicklaus Course. At the 15th, he rolled in a long putt for birdie and followed with a birdie at the 16th to reach 12-under.
At the treacherous par-4 18th, Leggatt made birdie to give his team the outright lead after the opening round.
'It's a good finishing hole,' Weir said of the 18th. 'You have to stand up there and hit a good tee shot, and that's the most important thing, is to get it in the fairway. The pin was in an easy spot today, but as the week goes on, it will be in trickier spots.'
Parry birdied the first three holes to give the Australians an early push and the duo continued to play well with three straight birdies starting at the sixth.
'Craig got us off to an ideal start,' said Scott. 'I just sat back and watched him.'
Parry and Scott were on fire on the inward nine as well with a stretch of four consecutive birdies from the 10th. They added a birdie at the 16th and Parry hit his tee shot to 18 feet for birdie at the 17th to move to 12-under.
'We could have had a couple of more birdies out there, there's no question about that,' said Parry. 'We left a couple out there. All teams are going to do that.'
Levet and Jacquelin had the lead heading to the par-4 last when they encountered the dangers of the closing hole. Both players found the hazard and then Levet had a difficult time placing his ball.
'I tried to place it at first on the flattest spot, but it was high in the slope,' said Levet. 'I thought it was going to stay easily, especially when I put it on quite the high grass, but it didn't.'
The ball rolled back into the hazard just off the green. Levet was given another chance to place it on his way to a double bogey.
'I could spend all day there if the ball starts to move all the time,' said Levet. 'Lucky we didn't get 65 on the last hole.'
Defending nation South Africa, represented this year by Rory Sabbatini and Tim Clark, finished three shots back at 10-under-par 62 alongside the Swedish duo of Niclas Fasth and Carl Pettersson.
Fiji's Vijay Singh teamed with Dinesh Chand for a 9-under 63. They finished four shots behind the leaders in a tie for seventh.
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