Sweeney joined the Labour Party in 2008 and first became an active campaigner during the 2009 Glasgow North East by-election. While working in the shipyards he joined the Unite and GMB trade unions, later joining PCS whilst at Scottish Enterprise. He is also on the executive committee of the Scottish Fabian Society. Sweeney came to prominence during the 2014 Scottish independence referendum, after he organised an open letter signed by young shipyard workers opposing the break-up of the UK, and subsequently spoke at a rally alongside Gordon Brownon the eve of the referendum. Sweeney's first experience of standing as an election candidate was in the 2016 Scottish Parliament election, where he placed twelfth on the Scottish Labour Party's regional list for West Scotland. At the 2017 general election he stood for Glasgow North East where a 12% swing to Labour led to him defeating Anne McLaughlin of the SNP by just 242 votes. McLaughlin had taken the seat from previous MP, Willie Bain of the Labour Party at the 2015 general election, and she had been elected with a 39% swing; which was the largest swing at the 2015 general election seen anywhere in the UK. The seat and its predecessors had previously been held by Labour MPs continuously since George Hardie was elected in 1935. On 3 July 2017, he was appointed by Labour leader Jeremy Corbyn as the Shadow Under-Secretary of State for Scotland. He made his maiden speech to the House of Commons on 13 July 2017, during which he expressed his opposition to Conservative austerity policies that had led to a fall in living standards. During the 2017 Scottish Labour leadership election, Sweeney endorsed Richard Leonard, who was ultimately the successful candidate. In November 2018, he won 'Best Scot at Westminster' in the annual Scottish Politician of the Year awards, in part in recognition for his lobbying of the Home Secretary and Prime Minister in asylum cases such as that of Giorgi Kakava, a ten-year-old orphan who had been threatened with deportation following the death of his mother. In 2019, he was cited as the least expensive MP in Scotland, including: office, staff and travel costs. Sweeney was one of 78 Parliamentarians who challenged the five-week prorogation of Parliament by Prime Minister Boris Johnson in the Court of Session. The case, together with a case brought in England and Wales by Gina Miller, was ultimately successful in the Supreme Court, resulting in the quashing of the prorogation on 24 September 2019. Sweeney lost his seat to the previous Scottish National Party MP Anne McLaughlin, at the 2019 general election with a marginal majority of 2,458 votes on a 4% swing, the closest result in Glasgow.
Outside politics
Sweeney has an interest in built heritage and architectural issues in Glasgow. He is a member of Glasgow Building Preservation Trust and has led walks as part of Glasgow Doors Open Days Festival for several years. Sweeney was also involved in the restoration of the historic former Govan shipyard head offices into the Fairfield Heritage Centre, for which he won an award. After campaigning against the demolition of Springburn Public Halls in 2012, he founded the Springburn Winter Gardens Trust, which is working to restore the nearby Springburn Winter Gardens.