Why didn't the British give representation to the 13 Colonies?

At that time in Great Britain, political representation in Parliament was restricted to a very narrow population: land-owning elite. Even relatively wealthy merchants and businessmen were denied the franchise, as they were thought to lack the necessary stake in the governance of the country due to the fact that their wealth was based on the ebb and flow of economic exchange rather than the fixity and stability of land.
As the vast majority of Englishmen were denied representation in Parliament, it didn't make much sense to the British government for American colonists of similar or lesser means to be given the same privilege. Successive British governments regarded the American colonists as little better than upstarts who had no business in running the country.
Besides, pro-British partisans never tired of pointing out that the American colonists already enjoyed a degree of autonomy over their own affairs far greater than that of anyone else in the British Empire.