Wedderburn’s father and grandfather fought for the Pretender at Culloden in the regiment raised by his maternal grandfather Lord Ogilvy. His grandfather was captured, attainted and executed, but his father escaped to Jamaica, where he set himself up as a medical practitioner. An inheritance from a great-uncle enabled him to acquire considerable property in the island and it was probably as a merchant and landowner that he made his fortune. John Wedderburn returned to Scotland in 1768 and the following year bought Ballindean and married. He continued to style himself a baronet, regardless of the attainder.
David Wedderburn’s mother died only two weeks after his birth, and when he was five his father married a distant relative of Henry Dundas. This connexion was later strengthened by Wedderburn’s own marriage to his stepmother’s niece and by that of his sister Margaret to Philip Dundas, Henry’s nephew. In 1796 Wedderburn joined the West Indian trading house of Wedderburn, Webster & Co. at 35 Leadenhall Street, London, which was run by his uncle and cousins and with which his father had done business from Jamaica. He took one-sixth of the profits which, in the prosperous years, were considerable. He was created a baronet in 1803, shortly after succeeding his father to Ballindean and property in Jamaica.
In 1804, he showed an interest in the venal Perth district of burghs, whose sitting Member, David Scott I, was in poor health. He eventually told Lord Melville, Scott’s close friend, that he had decided not to pursue it, but when Scott died, 4 Oct. 1805, he came smartly forward and secured the backing of the 9th Earl of Kellie, who had a strong interest in the constituency, but had earlier promised to support Scott’s son should his father vacate. Melville, who in normal circumstances would have remained neutral, sided with Scott and tried to make Kellie fulfil his commitment, but he failed to prevent Wedderburn from capturing three of the burghs. Wedderburn was able to reject Scott’s offer of a compromise and came in after the formality of a poll.
Shortly after his return he was noted as a new Member for inclusion in Pitt’s list of guests for birthday dinners.
Although he continued to give general support to government after 1812 his attendance seems to have become very irregular. His only recorded ministerial votes in this Parliament were on the army estimates, 8 Mar. 1816; the wartime salary of the secretary to the Admiralty, 17 Feb. 1817; the censure of the Scottish law officers, 10 Feb., and the employment of agents provocateurs, 11 Feb. 1818. His only recorded wayward vote was against the property tax, 18 Mar. 1816. He is not known to have spoken in the House and retired at the dissolution of 1818.
Wedderburn, who left the Leadenhall Street business in 1815, sold Ballindean about four years later. He served competently as Scottish postmaster-general from 1823 to 1831. For the last 30 years of his life he was involved in a complex lawsuit which, together with the abolition of slavery, eventually ruined the family business. He died 7 Apr. 1858.