I'm currently reading a book called American Nations which discusses the 11 rival "nations" in America and how they have evolved over time. I suppose that a simple answer to your question is that a lot of the British subjects of America appreciated the structure of the British government and the protection that it offered without really considering themselves to be British. They recognized that they were living in British territory but not all of them considered themselves to be "British." Not all of the inhabitants were from the UK and less were from Britain itself. A lot of the colonizers were German, Dutch, Scottish, Irish and from other Western European countries. The Irish/Scotsmen were tired of fighting in British wars, especially the somewhat recent English Civil War and wanted to get far away from the reaches of the crown. The German immigrants were also tired of war and sought a peaceful life of farming. The Dutch simply wanted to trade and stay away from war. Some of the ones who were actually British sought refuge in America based on religious freedom from the Anglican church.

Most of the colonies had been given the right to self govern for the first two hundred or so years, then suddenly lost that right preceding the Revolution. For some of the colonies, it wasn't that big of a deal to have provincial leaders or taxation appointed by the British Parliament, such as the Dutch (NYC), German (PA), and Deep South; for others it was tyranny, such as in New England, Tidewater region (Virginia/coastal Carolinas), and Appalachian regions (although the Appalachians were more split on the issue).

The Dutch had already ceded control to the British crown, so it wouldn't have been a big difference. The Germans had difficulty controlling their region, such as disputes between colonies, native populations, and the somewhat warlike Appalachian neighbors, and despite being great farmers they were shitty politicians so they welcomed the politicians who had experience. The Deep South was comfortable with the arrangement provided that slavery was not infringed upon. On the other hand, New England had prided itself on being independent and educated enough to promote its own leaders internally. The Tidewater region had a somewhat military based aristocratic structure and similarly had gotten familiar with promoting their own policies and leaders. The Appalachians were made up of people who generally distrusted the British crown but not all of them agreed with the idea of splitting off entirely from it. When it came to the Revolution, Appalachians were often disregarded by their Tidewater neighbors for being uncivilized and were barely even accounted for in the Continental Congress.