Why did britain begin interfering in the colonies affairs in 1763?

Because the want the colonialist to pay their national debt.

After a long war with Spain and France, victorious Great Britain had gained a vast global empire. The Treaty of Paris, signed in February 1763, brought an end to the world war and to the French Empire in North America. However, this war left the empire with a huge national debt. The British government started a project to force colonialist to pay higher taxes, or in other words, a "fair share" of the military expenses. Those new policies of taxes and acts led to a constant growth of resistance by the colonialists. In a final analysis, those were the very genesis of all American movements of independence.

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