Why did the british seek to control the American colonies?

It basically comes down to money.

Initially the British saw the colonies as an interesting distraction, however, after seeing the potential the was for agriculture and manufacturing they became competition. At that point Britain was in the midst of the Industrial Revolution and probably the most wealthy nation on earth.

In order to control/ regulate the "competition" as well as derive an income from the situation they instituted a number of taxes on goods originating from or produced in "the new colonies".

In some cases this saw goods exported from America (with the appropriate tax), taxed on entry into Britain, processed and then reexported back to America (again with taxes added on).

Ultimately this lead to dissatisfaction by the colonists which in turn resulted in various acts of rebellion (Boston Tea Party) which escalated into the War of Independence