Thomas King Weldon was born either at Cork or at Carrick-on-Shannon, County Leitrim, Ireland, probably some time between 1826 and 1829. He was the son of Patrick Campbell Weldon, an inspector of police, and his wife, Mary King. He married Eliza Simmons in Geelong, Victoria, Australia, on 24 November 1857. There were eight children of the marriage.
Weldon emigrated to Australia in the early 1850s and was one of the twelve members of the original Victorian Police Force cadet intake in December 1852. He reached the rank of sub-inspector within a few years, but with the retrenchment of that colony's force he headed a 10 man contingent of police sent to Otago at St John Branigan's request. He was appointed a sub-inspector in the Otago Provincial Police from 4 January 1862, and placed in charge of the four stations in the Dunedin district. This gave him the status of second in command to Branigan.
Although Weldon was contracted for a term in the Otago police, it was not long before he was secretly offered the post of inspector in charge of the Southland Provincial Police at a salary of £350. Concealing his reason for going, and declining an inspector's position in Otago, he resigned on 6 February 1863. At the same time the Southland government asked Branigan to recommend a suitable policeman from Victoria for the position, as an additional distraction to disguise his reason for leaving.
Weldon's appointment as inspector in charge of the Southland force commenced on 20 February 1863 with considerable expectations on all sides that this 'terror to evil-doers' would match the efforts of his previous leader in Otago. Branigan for his part refused to acknowledge Weldon as an equal.
On 9 March Weldon upgraded the main Southland gold escort – from Queenstown to Kingston by boat, then overland to Invercargill – into an 'imposing Victorian-style cortège', providing a service every two weeks. By 22 September he was designated Southland's commissioner of police.
However, all Southland's inducements to Otago gold prospectors and attempts to locate sizeable goldfields within its borders were to fail. By June 1864 the police force (which had reached a peak of 43 the previous year, with barracks able to house up to 65), was reduced to 28. This number fell to 18 by the beginning of 1865, and became only 11 by the end of March. Weldon was by now offering his services to other provincial governments, Nelson in particular. However, he remained in Southland until 1869, commanding a small, demoralised force. That year Branigan was appointed commissioner of the New Zealand Armed Constabulary Force, and left Otago for Wellington. Weldon succeeded him as commissioner of the Otago Provincial Police, a force which was soon to be augmented by the addition of the members of the Southland police, on Southland's reincorporation with Otago in 1870.
Weldon was to continue as a senior police officer in Dunedin for a further 20 years. When Branigan died in 1873, Weldon was an unsuccessful contender to succeed him as commissioner of the New Zealand Armed Constabulary Force. However, when the New Zealand Constabulary Force was created from the previous provincial forces and the armed constabulary force in 1877, he became for a few years superintendent of constabulary in charge, South Island, still based at Dunedin. This position was abolished in a restructuring, but Weldon stayed, heading the Otago–Southland Police District as an inspector, after the creation of the New Zealand Police Force in 1886, until his retirement in 1890.
Weldon lived in Dunedin in his retirement and died there on 15 June 1894. He is buried in the Southern Cemetery, Dunedin.