On the 29^th October 1997, shortly after his election to Ballymena Council, Tweed was fined at Coleraine magistrates court for assaulting a man in a pub.

On the 8^th June 2006, at a Ballymena Borough Council meeting, Tweed said that he "questioned the upbringing" of a 15-year-old Catholic, Michael McIlveen, who had recently been murdered in Ballymena in a sectarian attack. He also claimed people linked to the victim's family had been involved in intimidation of Protestants after the murder.

On the 22^nd September 2007, Tweed was stopped while driving a car under the influence of alcohol. On the 21^st January 2008, North Antrim Magistrates Court banned him from driving for a year and handed down a £250 fine.

In January 2009, Tweed was charged with ten sex offences against two young girls, spanning an eight-year period; he was acquitted in May 2009.

He was acquitted on the 27^th November 2012 of one charge of indecent assault on a child.

Tweed was convicted on 13 counts of gross indecency, indecent assault of two young girls and inciting gross indecency, spanning an eight-year period from 1988 onwards. His conviction was quashed on the 25^th October 2016, due to issues around presentation of evidence of bad character. As he had served almost 4 years in prison he was not retried.

In November 2021 Tweed's stepdaughter Amanda Brown spoke on BBC Radio Ulster TalkBack programme, of the alleged sustained sexual abuse she suffered at his hands. She questioned the appeal process and explained the reason she was unable to face a further court case. Amanda called on the prominent politicians who eulogised him at the time of his death to reconsider their remarks. Her siblings have also spoken of their alleged experiences of Tweed's sexual abuse, Victoria and Catherine Alexander Tweed waived their right to anonymity to speak of this abuse.

After the conviction was announced the Orange Order terminated his membership of the organisation. The Royal Black Institution, of which Tweed was also a member, stated it had begun the process of expelling him from its membership. Pending sentencing he remained a member of Ballymena Borough Council and of the TUV, although the party announced on the 15^th November 2012 that it had 'suspended' his membership "not because we doubt his innocence, but because this is what the party rules require." The TUV noted that the sex offences related "to a period long before he was a member of this party". The TUV chose one of its unsuccessful 2011 candidates, Timothy Gaston, to replace Tweed as a councillor.

Tweed died in a motorcycle crash on the 28^th October 2021 in County Antrim, at the age of 61.

Following his death, members of his family, and the victims of his now-quashed conviction due to lack of evidence, have spoken of the effect on them of his alleged sexual and physical abuse.