Dressler was born in Bismarck, North Dakota to Rick and Val Dressler. He attended Bismarck High School. At Bismarck he was a three time all-state and all-conference selection and in 2003 was named North Dakota Gatorade High School Player of the Year. On March 23, 2009, his Bismarck high school retired his jersey (#2).

Dressler went undrafted in the 2008 NFL Draft and signed as a street free agent with the Saskatchewan Roughriders on May 13, 2008. After the Roughriders named their final cuts, Dressler was one of five rookies to make the final team. After two games with the Roughriders he led the league with 13 punt returns for 185 yards. However his receiving yards had been accidentally omitted by the CFL’s statistical package. On July 14, Dressler suffered a hamstring injury that forced him out of the lineup. Towards the end of the season, Dressler was being considered as the leading candidate for the CFL West’s nomination for rookie of the year. As of October 18, Dressler had 46 catches for 928 yards with five touchdowns including six 100+ yard games. On November 5, it became official and Dressler was nominated for rookie of the year. Dressler later won the award over Hamilton’s Prechae Rodriguez. Dressler finished the season with a team-leading 1,123 yards receiving (11th overall) and 2,219 combined yards (3rd overall). At the end of the 2008 season, he was voted the most popular player by the fans.

Ensuring that there would be no sophomore slump, Weston Dressler had the most receiving yards in a game in his young career when he caught seven passes for 154 yards against the BC Lions in the home opener. Because of his value as a receiver, the Roughrider coaching staff pulled him from the kick return game and only used him in critical situations on special teams. Ken Miller, the Saskatchewan head coach, and Paul LaPolice, the offensive coordinator, used many different formations in order to get Dressler the ball, from the slot back position, to wideout, to handoffs. On August 21, 2009, against the Montreal Alouettes, Dressler caught eight passes for 179 yards, his most yards gained in a single game to date. On Oct. 10, 2009, Dressler’s season came to a close as he sustained a sprained right ankle and fractured right fibula in the closing minutes of a win over the Toronto Argonauts, halting his receiving yardage total under 1,000 yards.

In the ensuing four seasons, Dressler’s receptions exceeded the 1000 yard mark every year. In 2013, Dressler was a CFL All Star and won the 101st Grey Cup. On January 30, 2014, Dressler was released from the Saskatchewan Roughriders so he could sign with a National Football League team.

On February 5, 2014, Dressler signed a futures contract with the NFL’s Kansas City Chiefs. He was waived on August 25.

In his return to Saskatchewan on August 31, 2014, Dressler had three receptions for 28 yards in a 35-30 win over the Winnipeg Blue Bombers in the Labour Day Classic. During the Banjo Bowl against the Winnipeg Blue Bombers, Dressler returned a punt for a touchdown, his second of his CFL career. On September 21, 2014, Dressler recorded 125 receiving yards in a win over the Ottawa Redblacks, a game where he returned another punt for a touchdown. Dressler tied the all-time number one record (CFL and NFL) for the most two point conversions caught in a single game by one player at two in a 31-24 loss to the Calgary Stampeders on October 3, 2014. He wound up playing in the final 9 games of the 2014 season and the Riders lone playoff game. On January 30, 2015, Dressler re-signed with the Roughriders, agreeing to a new 4-year contract extension.

On January 16, 2016, the Roughriders released Dressler.

On January 26, 2016, the Winnipeg Blue Bombers announced that they had signed Dressler to a two-year deal through the 2017 CFL season. In his first year with the Bombers he played in 16 games, and broke the 1,000 receiving yard plateau for the sixth time in his career. In 2017 Dressler played in 11 games, caught 51 passes for 691 yards with three touchdowns. Dressler played the first half of the 2018 season before being placed on the six-game injured reserve with a lower-body injury. On October 26, 2018, he caught a pass that put him over the 10,000 receiving-yard mark, becoming the 17th player in league history to accomplish that feat. Dressler was notified prior to the 2019 CFL free agency period that he will not be offered a contract with the organization, making him a free agent after three seasons with the team.