The Treaty of Paris was signed in 1763 and formally ended the French and Indian War, which was a war primarily against the French and Great Britain.
The Treaty of Paris gave the territories in North America that the French had to Great Britain. France no longer had any territories in North America except a small part of Louisiana. They generally accepted this and did not fight against Great Britain. This meant that there was no threat for the colonists any longer, except the Native Americans, which Great Britain made sure to provide troops to defend against.
Along with this, the Treaty of Paris recognized the independence of the colonists. Westward expansion was taken up by a lot of people, as so much new land had been acquired.