Before entering politics, Kweon worked as a prosecutor and lawyer at various prosecution offices and the Ministry of Justice.

[1] He is the eldest of the three sons and a daughter of a housewife and Kweon Seung-ohk (died in 2022), was an educator and the former Director of Gangneung Myeongryun Institution.

[1] Although Kweon participated in anti-dictatorship movements in 1980, he chose to prepare for the bar instead of continuing his activism as he did not agree with "radical changes".

[2] In the 2008 election, Kweon made an unsuccessful attempt to contest for Gangneung under the Grand National Party (GNP) banner.

[1][2] On 8 April 2022, Kweon was elected parliamentary leader of the People Power Party, defeating Cho Hae-jin.