Jay Bouwmeester, selected to the Eastern Conference all-star team earlier in the day, had two goals and two assists for Florida. Chris Gratton and Rostislav Olesz also scored for the Panthers, and Ed Belfour had 14 saves.
Alexander Semin, Matt Pettinger and Chris Clark scored for Washington, which lost its fifth straight on the road. Olaf Kolzig gave up five goals on 41 shots before being replaced by Brent Johnson at the start of the third. Johnson made 10 saves on 12 shots.
The 53 shots were a season high for Florida, which has won four straight at home.
Washington pulled to 2-1 as Semin poked in a rebound under Belfour's leg at 11:56 of the second for his 25th goal of the season.
Florida stretched its lead to 3-1 about one minute later on Weiss's first goal. Kolzig blocked a shot by David Booth but Weiss picked up the rebound and beat Kolzig.
The Panthers added two more goals in the second. Olesz scored on a power play at 17:33 when he stopped a pass with his foot and one-timed it into the net. Bouwmeester's second goal of the game, a shot from the top of the circles, stretched the lead to 5-1.
Weiss's second goal came on a breakaway as he put the puck between Johnson's legs to make it 6-1 at 4:23 of the third.
Pettinger's short-handed goal at 10:09 of the third pulled the Capitals to 6-2. Weiss scored his third goal less than a minute later, and Clark's goal came in the final minute.
The Panthers scored 1:35 into the game as Bouwmeester brought the puck into the right circle and his wrister went over Kolzig's blocker. Gratton made it 2-0 at 12:46 of the first, taking the rebound of Olli Jokinen's shot and pushing the puck past Kolzig.
Notes: Jokinen has 10 assists in his last 13 games. His first-period assist was his first point against the Capitals in five games. ... Belfour is 6-1-2 since Dec. 16.