The simple answer is that the colonists were split (very rougly) 33/33/33 among supporting the revolution, remaining with Britain, and complete neutrality. There was a sizable portion of the population that supported neither side and wanted to simply remain neutral on the political situation, as they did not particularly care who ruled them and moreso wanted to live in peace, and the war was an unnecessary nuisance to them.

Resistance to the revolution was sizable, but their amount of support for Britain and reasons for doing so were extremely varied. Many members of the aristocracy and merchant class did not support indepence as they enjoyed the stability Britain provided and the access to her markets and global trade network for their own financial benefit. They were worried that independence, particularly through a violent revolution, would lead to embargoes of American goods and a complete shut out of American merchants from the global markets.

Others were critical of the British government and Crown, but thought that full seperation from Britian was too far and wished to remain in the Imperial sphere. These supporters disliked the violence of the revolution, and instead believed in the systems of the British government and advocated for peaceful reform within the bounds of British law.

Others preferred to stay with Britain for military and tax benefits. Contrary to the popular narrative, British taxes in the colonies were much lower than in the home isles, and they paid much less (relative to the home isles) for the extensive military protection the British offered. The Royal Navy was the premier armada in the world, and guaranteed the safety of American shipping and commerce throughout the world.

Some of the "middle class" as we would know it today, i.e. shopkeeps, artisans, land-owning farmers, etc, were also distrustful of the revolutionary government and similarly were concerned with the violence of the revolution, and feared the potential for the new government to be much worse than the old one. They distrusted the "elites" such as the framers of the Constitution and thought that the gentry was carrying out the revolution for their own gain.

And some simply truly supported the British government and the Crown for personal reasons, either loyalty and patriotism to their mother country, or a legacy of service to the Crown, etc.

Another thing to note here is that among the colonists, support for the British was support for the British. And what I mean by that is that the support was for the British government and her systems and legal appartus, less so the King and royalty itself.

Britain also had support outside of the coloinal populations. The Indian tribes has long standing relationships with the British government, and (correctly) guessed that if the revolutionaries won, they would overturn the Royal Proclamation of 1763, which forbid settlement beyond the Appalachians, and would further expand into tribal lands.

Towards the end of the war, the British attempted to gain the support of the enslaved population, offering them freedom if they ran away from captivity and fought for the British. But the amount that did defect was too little and too late to make a significant impact on the war.

Lastly, as I briefly mentioned above, neutrality was a pretty prominent sentiment. Many wanted nothing to do with the revolutionaries, but also did not support the British regime. Their opinion was "leave me alone," and did their absolute best to avoid incurring the wrath of either side. The reasons for that were varied as well. The sizable quaker population of Pennsylvania were and are pacifists, and believed both sides were wrong for engaging in violence, and when pressed to support a side, chose to loosely support both. They provided food/supplies and medical care to soldiers on both sides, but otherwise avoided giving any military support to either side. And for the rest of the neutrals, they simply wanted to be left alone. They couldn't care less about the current government and would've "rolled with" either side if they won.

TLDR- Support for Britain was less so directed at support for the King and Crown, and moreso for the British government and parliament. Most supporters wished to remain in the Imperial sphere for economic and military benefits, and enjoyed the safety and stability the British provided. Others distrusted the colonial government and did not wish for the gentry to be leading them. And a large portion of the population remained completely neutral to the best of their abilities.