Lord Chancellor of Ireland
On 12 January 1559, Weston was created Dean of the Arches and was a commissioner for administering the oaths required of ecclesiastics under the Act of Uniformity. He was consulted in regard to the Queen's Commission issued on 6 December 1559 for confirming Matthew Parker as Archbishop of Canterbury and was included in a commission issued on 8 November 1564 to inquire into complaints of piratical depredations committed at sea on the subjects of the King of Spain.
The Lord Deputy of Ireland, Sir Henry Sidney, requested that Weston be nominated for the post of Lord Chancellor of Ireland in succession to Hugh Curwen, Archbishop of Dublin, in April 1566. After a year, on 10 June 1567 Queen Elizabeth told Sidney that after good deliberation she had made the "choice for the supply of room of Chancellor by naming thereunnto our trusty well-beloved Doctor Weston, dean of the arches here, a man for his learning and approved integrity thoroughly qualified to receive and possess the same" and "that for some increase of his living whilst he remaineth in our service there she was pleased to give unto him the Deanery of St Patrick's, whereof the Bishop of Armagh (Adam Loftus) is now dean and yet to leave it at our order, as we know he will".
Weston arrived in Dublin early in August and was sworn into office on 8 August 1567. He was conscientious in performing his duties, and greatly respected for his integrity, although ill-health (he was plagued by gout and gallstones) hampered his effectiveness. He was appalled by the laziness and inefficiency of many of the Irish judges and urged Elizabeth to replace them with Englishmen wherever possible. He was equally shocked at the poverty and ignorance of many of the Protestant clergy in Ireland. His zeal for reform led him, though a layman, to become an effective leader of the Church of Ireland for a few years. He cooperated with Adam Loftus, now Archbishop of Dublin, in purging the Archdiocese of Dublin of crypto-Catholics, but was opposed to the persecution of the Roman Catholic majority, or any efforts to forcibly convert them.
Weston and Sir William Fitzwilliam the Vice-Treasurer of Ireland were sworn Lords Justices in Christ Church Cathedral, Dublin on 14 October, and he became a member of the Privy Council of Ireland. Weston addressed the Irish Parliament when it was summoned on 17 January 1568.
In addition to being Dean of St Patrick's, he was Dean of Wells from 1570 to 1573, but his health was failing.
