The long-hitting lefty shot a 3-under 67 to maintain the two-stroke lead he took with an opening 62.
''[Thursday] I added it up after I left the media center, I had three holes I didn't have a wedge into,'' he said. ''Today was different, because the wind conditions were different. They were faster and it was coming from a different direction, so it made the golf course a little bit tougher.''
Watson won his first PGA Tour title at the 2010 event and has finished in the top 20 five times in eight previous starts. He tied for sixth in 2008, tied for second in 2012, and finished fourth in 2013.
He was delayed in talking to the media Friday after being pulled for a random drug test, something he saw as a positive sign.
''I hope I passed it,'' he joked. ''It's usually when you're at the top of the leaderboard they want to drug test you, especially me.''
Stuard, who followed an opening 64 with a 67, pulled within a shot of Watson after back-to-back birdies on 15 and 16. But he bogeyed the 17th after hitting his second shot over the green and missing an 8-foot par putt. He then saved par on the 18th with a 19-foot putt.
''That was kind of a nice momentum-keeper going into the weekend,'' he said.
Pettersson started on the back nine and shot a 31 on those holes before finishing with a 66.
The back nine was less affected by the wind than the front, where a headwind had several holes playing longer than their yardage.
Scott Brown had a double bogey on his first hole and posted a 38 on the front. But after making par on the 10th, he reeled off six straight birdies to finish with a 67. He was 8 under, tied for fifth place with Jason Gore and Chris Stroud, who is still looking for his first tour win after losing here in a playoff to Ken Duke in 2013.
''The back nine always plays a bit easier here anyway, so I knew there were going to be some opportunities out there,'' Brown said. ''So I just kind of hung in there. When my caddie said, 'Let's go get them on the back nine,' that's what we did.''
Thirty-three players were within six shots of the lead.
Ernie Els, who shot a 66 in the opening round, bogeyed the first five holes and missed the cut after shooting a 76 to finish 2 over after 36 holes. Els, making his first appearance here since 2002, threw his club into the air in frustration after bogeying the 12th hole and hitting his tee shot on the 13th left and into the water guarding the green.
Others notable names who failed to make the cut include Stewart Cink (139), who has won this tournament twice; defending champion Kevin Streelman; four-time major champion Padraig Harrington (141), 2007 winner Hunter Mahan (141) and Louis Oosthuizen (142).
Representatives from the British Open brought the claret jug to display at the Travelers on Friday, as a reminder to players that four spots and as many as nine in that tournament are up for grabs this week.
The leading five players, not already exempt, from the top 20 in the FedEx Cup will be part of the field at St. Andrews next month.
In addition, the leading four players who finish in the top 12 at TPC River Highlands also will get spots. The Travelers is the first of three PGA Tour events where top finishers can get into St. Andrews. There are four spots available at The Greenbrier Classic, and one at the John Deere Classic.
''I've been in professional golf for 18 years now and I've never been to Europe,'' Gore said. ''So that just blows my mind. It blows a lot of people's mind. Playing at St. Andrews would be a lot of fun, but we've got a long way to go.''