He was named 2003 Danish Player of the Year, and received a 2003 Olympic Committee fair play award for missing a penalty kick on purpose.

He took part in the 1992–93 UEFA Champions League qualification games against Scottish team Rangers in September 1992,[3] and moved to play in Scotland shortly thereafter.

[5] In the 1997–98 season, Wieghorst played 31 of 36 league matches for Celtic[6] as the club won its 36th Scottish championship to end "Old Firm" archrivals Rangers' nine-year stranglehold on the title.

In 2000, Wieghorst was diagnosed with the Guillain–Barré syndrome, and following treatment he spent a year in recovery before returning to play in a November 2001 Scottish Cup game.

He returned to the starting line-up late in the 2004–05 season in April 2005, and was a part of the Brøndby team that won The Double of both league championship and cup trophy.

He made his debut for the Denmark national team in August 1994,[10] when he came on as a half-time substitute and scored the deciding goal in the 2–1 friendly match win against Finland.

He was a part of the Denmark squad that won the 1995 King Fahd Cup, where he came on as a substitute to replace the injured team captain Michael Laudrup in the 2–0 final win against Argentina.

[12] In the game against Iran, an Iranian player mistook a whistle from the crowd as being the referee's half-time signal, and picked the ball up with his hands in the penalty area.

Wieghorst managed Nordsjælland to a run in the 2008–09 UEFA Cup defeating TVMK Tallinn from Estonia and Scottish club Queen of the South,[15] before they were eliminated by Greek side Olympiacos.

[17] On 7 February 2013, it was reported that he would join Swansea City as an assistant to club manager Michael Laudrup.

[18] On 4 February 2014, Swansea fired him alongside Michael Laudrup, just three days short of his year anniversary in the job.

[23] On 12 June 2019, it was announced that Wieghost would be assistant to Kasper Hjulmand at the Danish national team starting in July 2020.

[25] When Hjulmand resigned following the UEFA Euro 2024, Wieghorst was made new manager of the national team on a short term contract running for the rest of 2024.

[26] He never managed the team in a competitive game, since he had to go on sick leave on 26 August 2024, and he was replaced as caretaker by Lars Knudsen.