He studied law in England and returned to Saint Christopher where he served as speaker of the house of assembly, attorney-general and chief justice.

He was the son of Eliza Anne (née McTair) and George Henry Burt, a sugar planter from a prominent family on the island.

[1] Burt likely spent his earliest years on his father's plantations, possibly on the Brothersons estate of 300 acres (120 ha) in the Capisterre district.

[1] He was sent to England to attend a private school in Richmond, Surrey, and was then admitted to study law at the Middle Temple in April 1825, aged 14.

Sir Archibald began to look elsewhere for judicial office, eventually accepting the post of Civil Commissioner and Chairman of Quarter Sessions in Western Australia.

In the early years of the court, Sir Archibald was conspicuous for his support of maintaining the division between barristers and solicitors, and also for his domination of the legal fraternity.

Despite widespread criticism of this action, Sir Archibald remained implacable in his defence of his duty to protect the integrity of the Court.

As his tenure continued, Sir Archibald gave up any hope of returning to the West Indies, and despite failing health during his last years, remained Chief Justice until his death in November, 1879.

In 1836, Burt married Louisa Emily Bryan, the daughter of a local physician, at St. George's Anglican Church in Basseterre, Saint Christopher.

His seventh son Septimus became attorney-general of Western Australia, while his daughter Louisa married George Leake, who became the state's third premier.