Should be noted that the colonization of America and its gradual ascension to become the world's most powerful country is one of history's biggest accidents.
To give the short version, the early European empires saw North America as one of two things, a dumping ground for its unwanted heretics and a convenient conduit to conduct trade with more lucrative markets, nothing more.
Britain was the most powerful empire in the planet at the time, they could've kept onto its American colonies if it was willing to expend the manpower. Less we forget, towards the end of the war the majority of redcoats who fought against the thirteen colonies were themselves colonists who stayed loyal to the crown. But in the end, it was a loss they swallowed because the thirteen colonies were a backwater compared to say the Carribean colonies, which made Britain obscenely rich thanks to tobacco, or the crown jewel that was India.
