In 1780, there was virtually no British Empire.
British possessions were composed only of the 13 colonies, the Atlantic Canadian coast and some caraibbean islands.
Look at this map, what you can see in orange is what the British Empire was like in 1780:
http://www.bbc.co.uk/history/british/empire_seapower/images/porter_british_empire_1815_map.gif

The British Empire as we know it was built between 1850 and 1880 by attacking and annexing the lands of various defenseless tribes in Africa and Asia.
At the times the American Revolutionary War occured, Britain was just the lesser of european power (below France, Spain, Austria, Russia and Prussia) and in no way a superpower ruling over 1/3 of the world.