It may be noted that although popular US history often describes Great Britain as the mightiest power in the world at the time, Britain was rather puny in the size and power of its army.
The Chinese Empire and some other Asian powers had armies in the hundreds of thousands, and at least four European powers, France, Russia, Austria, and Prussia, also had armies in the hundreds of thousands and far better trained and equipped than Asian ones. Thus the major military powers of Europe had armies at least four or five times larger than Britain's.
Minor powers like the larger German states often had armies in the tens of thousands, and thus roughly in the same league as the British army.
Landgrave ("count of an entire land") Frederick of Hesse-Kassel sent the largest contingent of "Hessian" allies, but there were also troops from other states.
They included Hesse-Hanau, ruled by a son of Frederick of Hesse-Kassel, the Margravites ("border counties") of Brandenburg-Ansbach and Brandenburg-Bayreuth (ruled by a cousin of the King of Prussia), the Principality of Anhalt-Zerbst (ruled by the brother of Empress Catherine the Great of Russsia), The Principality of Waldeck, the Duchy of Brunswick-Wolfenbuttel (ruled by a cousin of King George III), and the electorate of Brunswick-Luneburg (Hanover) where negotiations were made easier by the Elector being King George III himself.
What the British really needed was to ally with one of the major military powers, such as France, Russia, Austria, or Prussia, to get a really large reinforcing army, but that did not happen.
The French were soon allied with the Americans, the Austrians were technically allies of the French and might possibly also have supported the Americans in slightly different circumstances, Austria and Prussia were distracted in 1777 by fighting the brief "Potato War", and the League of Armed Neutrality in 1780-1783, protesting the British searches of neutral shipping, eventually included Russia, Sweden/Finland, Denmark/Norway, Prussia, Austria, the Ottoman Empire, and both Sicilies, almost every major European state that wasn't already allied to or at war with Britain.