What effect did the American war of independence have on the British Atlantic Empire?

Needless to say, the American Revolution represented a major trauma to the British Atlantic Empire, as Britain lost a significant portion of its colonial holdings. Beyond those colonial losses, however, the experience of the American Revolution did not halt the subsequent expansion of British economic and political power, with Britain eventually emerging as the premier superpower of the 19th century.
Most notably, Britain did seem to take some lessons from the experience in the American Revolution. If we were to look towards the example of Quebec, as resistance in the thirteen Colonies intensified, British Parliament abolished the Test Act in the colony and granted the Catholic Church official status within Quebec (out of recognition of the Catholic majority). A later act of Parliament (in 1791) created a more centralized colonial administration over Canada. Similarly, we could look towards India and 1784's India Act, which installed greater Parliamentary oversight over the East India Company. The post-Revolutionary War period was an era of dramatic economic growth and imperial expansion. Even as the Atlantic Empire was severely diminished, Britain's global power was still in ascendance.
Citation note: see John Merriman, A History of Modern Europe: from the Renaissance to the Present (3rd edition), New York: W. W. Norton, 2010. See pages 418-419.