For example, the UK had to leave its holdings in India, and the Cold War was then 'fought' primarily between the US and the USSR. Why was the USSR not weakened in a similar fashion to the UK by WW2?
The very short answer is that the the 6 years of war hurt the British bank balance and as the colonies became financial sink holes it made more financial sense to allow them independence. Their was also an increasing struggle for independence from the colonies. Soldiers who came to Britain to fight for the empire had a better living standard and a better quality of life in the army than they did back home prior to the war, this further fueled their desire for independence.
The USSR on the other hand forced their power upon the eastern European countries they liberated from the Nazis. Fearing a resurgent Germany they wanted to keep Germany as weak as possible and create a buffer between western Europe and Russia in which to fight any future invasion.