An online list of ministers of Blackfriars does not include James Waugh, however I also found this:
"The first minister of Spring Garden Lane Secession (Burgher)
Church was the Rev. James Waugh. Garbutt states that he was
sent by the Synod at the request of the congregation and
approved of by them. He was ordained by the Presbytery of
Edinburgh, there being then no organised Presbytery in the
north of England in connection with the denomination. Mr.
Waugh came from the congregation of Blackfriars, Jedburgh,
and was in his 32nd year when ordained. After a ministry of
20 years he died in July, 1786. Not much is known of his
ministry, but Gartnitt says it was highly acceptable and the
congregation increased. His life is described as laborious and
indefatigable"
I take that to mean that he was a member of the congregation of Blackfriars, but not its minister, and that he was subsequently ordained, presumably by the Associate Presbytery of Edinburgh rather than that of the Church of Scotland.
National Records of Scotland, Ref. CH3/568/59, Miscellaneous papers: includes Printed petition signed by session and trustees of congregation in Sunderland, James Waugh, minister, of the burgher church there, for financial assistance. 25 February 1775.
"Registers of the Secession Churches in Scotland" compiled by Diane Baptie, available from SAFHS
http://www.safhs.org.uk/publications.asp, might help in the search for James Waugh's marriage if a record exists.