why did the french and indian war affect the british

"The French and Indian War" is a term only really used in the United States. It refers to only part of a broader conflict, the Seven Years' War, in which Britain, along with much of Europe, was embroiled from 1756-63. Remember that at this point in time, America did not exist as a nation, so the French and Indian War, or the North American front of the wider conflict, was really a war between French and British colonists, a reflection of the European conflict between France and Britain. It affected the British because British colonists and their Native American allies were the primary combatants against French colonists in their dispute over land. At this point in time, these people were British citizens.
In terms of mainland Britain, it also affected the British at home because the wars overseas had to be financed and were very expensive. Indeed, the huge amount of money the British government had apportioned to defending its North American colonies was highlighted as a reason against revolution in the United States, the argument being that Britain had helped the colonists defend their territories, at great cost to itself, and deserved their loyalty. The huge tax hikes that followed the Seven Years' War, which caused such agitation in the colonies, were in large part a result of expenditure in North America: Britain's national debt was now enormous and the government was seeking to recover it. So, this war affected Britain's economy significantly, and also contributed to the loss of the North American colonies it had spent so much money in defending.