He was the eldest son of John Hay, 1st Earl of Tweeddale (created 1 December 1646) and Lady Jean Seton.

[1] After his mother's death a few days after his birth in 1625, his father remarried to Lady Margaret Montgomerie, the eldest daughter of Alexander Montgomerie, 6th Earl of Eglinton and Lady Anne Livingston (eldest daughter of Alexander Livingston, 1st Earl of Linlithgow).

[2] He used his influence to moderate proceedings against the Covenanters, but with the hardening of the official attitude in 1674 he was dismissed from office and from the Privy Council on the advice of Lauderdale.

As Lord High Commissioner to the Parliament of Scotland from 1694 to 1696 he ordered the inquiry into the Glencoe massacre in 1695.

[4] On 4 September 1644, Tweeddale was married to Lady Jean Scott, the second daughter of Walter Scott, 1st Earl of Buccleuch and Lady Mary Hay, third daughter of Francis Hay, 9th Earl of Erroll).