Sweeney studied for a degree at the University of Glasgow, where he graduated with a first class MA (Hons) in Economic History and Political Science in 2011.

[9] After an internship with BAE Systems at Portsmouth Naval Base as an undergraduate, Sweeney joined the company's graduate development programme with BAE Systems Maritime – Naval Ships in 2011,[10] based at the Govan and Scotstoun shipyards on the Clyde, where he undertook a series of roles in production engineering and shipbuilding operations management on the Type 45 destroyer, Queen Elizabeth-class aircraft carrier and Type 26 frigate programmes, including co-authoring a 2014 publication on the construction programme for the Type 45 destroyer.

[13][14] At the end of 2015, Sweeney joined the national economic development agency Scottish Enterprise as a senior executive, working with the leadership of companies across the defence, marine, shipbuilding, aerospace and engineering sectors based in Scotland.

[23] 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, overturning a 25% majority of 9,222 in an unexpected result, having not even prepared a victory speech.

[31] He was a critic of the seven Labour MPs who defected to form Change UK in February 2019, describing them as "self-centred careerists" at a meeting which took place the following month to mark the relaunch of Tribune magazine.

[32] In November 2018, he won 'Best Scot at Westminster' in the annual Scottish Politician of the Year awards,[33] following his lobbying of the Home Secretary and Prime Minister in asylum seeker rights cases such as that of Giorgi Kakava, a ten-year-old orphan who had been threatened with deportation following the death of his mother,[34] the Kamil family who had been left without status for 18 years,[35] teenage brothers Somer and Areeb Umeed Bakhsh,[36][37] who were also supported by the Labour Party leader Jeremy Corbyn during a visit to Possilpark in August 2018,[38] and trafficking victim Duc Nguyen.

[47] 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.

[48] After losing his seat, he went on to work on Angela Rayner's successful campaign in the 2020 Labour Party deputy leadership election.

[51] During the COVID-19 pandemic, Sweeney revealed he had begun applying for Universal Credit in May 2020,[49] saying "The reality is, the majority of Scots are working class – if they stopped earning a salary, within two months they'd be in financial difficulties.

"[52] He later wrote an article describing his experiences of life on social security in December 2020, stating "I will admit that I’ve occasionally had suicidal thoughts in my darker moments over the last few months."

[64] A supporter of drug policy reform whilst an MP,[65] in March 2020 Sweeney announced that he was supporting activist Peter Krykant in his efforts to open an unsanctioned supervised overdose prevention site in Glasgow in an effort to persuade the Lord Advocate and Scottish Government to introduce a legal framework to regulate their official operation, in a similar manner to needle and syringe programmes.

[71] In leaked WhatsApp messages, the "soft Brexit" position taken by Scottish Labour in its 2019 European Parliament election campaign was criticised by Sweeney, who wrote, "If it's like this then it's a bad misjudgement and I'm having nothing to do with it... Let's hope the NEC [National Executive Committee] kill this bullshit line.

[77] He supports replacing the first-past-the-post voting system for the House of Commons with proportional representation and is a member of the Labour Campaign for Electoral Reform.

[78][79] Sweeney opposed Home Office contractor Serco[80] evicting hundreds of asylum seekers from their accommodation across Glasgow,[81][82][83] In 2019 he committed Labour to ending unlimited immigration detention in prison-like facilities, including Dungavel.

[85] In December 2021, he launched a campaign to extend the Scottish National Entitlement Card eligibility for free bus travel to all asylum seekers resident in Scotland, arguing that the vast majority were fleeing wars and persecution, but until their applications are determined they are not allowed to work, are subject to "no recourse to public funds" visa restrictions and are forced to live in "slum-like" accommodation, with just over £5 a day to live on.

[87] In the wake of a series of veteran suicides in the summer of 2018, including from his former regiment,[88] He has criticised the British Army and Ministry of Defence for inadequate mental health support for former soldiers, and a lack of sufficient records to establish the scale of the problem, accusing them of ‘passing the buck’ to overstretched military charities like Combat Stress.

[90][91] Sweeney also successfully campaigned to restore the Highland Light Infantry memorial in Kelvingrove Park after it was vandalised in February 2019.

[107] He called for greater investment in improvements to the Clyde's shipyard infrastructure,[108] a long-term continuous shipbuilding programme from Defence Equipment and Support,[109] condemned delays to Type 31 frigate procurement,[110] and was part of a successful campaign to get acommitment from the Ministry of Defence that the Royal Fleet Auxiliary's planned Fleet Solid Support Ships are built in British shipyards.

[122] An £8 million restoration programme by Collective Architecture to convert the building into a major events and performance venue was unveiled by the Trust in October 2020.