The colonies were a burden. They were useful for military and political reasons, but not for economic reasons. The reason Europe is so wealthy is Capitalism and early industrialization. The reason the colonies are so poor is colonialism.
But it seems to miss the point that capitalism requires cheap resources and also markets, and the European countries got these resources at huge concessions from the colonies which also provided a market for them. For example the British used Indian tax to buy cotton with tax collected from India, send it to the industrialised production centres (while deliberately destroying the traditional ones in India), and then sell it back to the Indians.
An easier way to understand it is imagine if the US got a 5% discount on Chinese imports -- would that help the US economy? British got close to a 90% discount (by force) on imports from India.
An easier way to understand it is imagine if the US got a 5% discount on Chinese imports -- would that help the US economy? British got close to a 90% discount (by force) on imports from India.