On 28 November 2012, he 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 25 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. Brown 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.
