He was one of the commissioners to a treaty with the Albany Indians in 1745 and 1755, and he and his colleagues effected the purchase of several million acres comprising the southwestern part of Pennsylvania.

Norris proposed that its inscription should be: "Proclaim liberty throughout the land unto all the inhabitants thereof," based on the Bible's book of Leviticus, chapter 25, verse 10.

During his speakership, the colonial representatives and the proprietaries had a long conflict about the taxation and legislative control of the Penn family estates.

'"[citation needed] In 1754, he was selected as a member of the Pennsylvania delegation, led by Benjamin Franklin, that attended the Albany Congress, a gathering of numerous colonial representatives to plan an approach to their defenses before the pending French and Indian War, the North American front of the Seven Years' War between Great Britain and France.

In 1757, Norris was appointed with Benjamin Franklin as a commissioner to England to work for the removal of grievances related to the proprietary instructions, but declined on account of failing health.

Norris was an excellent French, Latin, and Hebrew scholar, collected a valuable library, and was active in educational and benevolent enterprises.