Why the 13 colonies are a net loser for Great Britain:

A great empire has been established for the sole purpose of raising up a nation of customers who should be obliged to buy from the shops of our different producers all the goods with which these could supply them. For the sake of that little enhancement of price which this monopoly might afford our producers, the home-consumers have been burdened with the whole expence of maintaining and defending that empire. For this purpose, and for this purpose only … a new debt of more than a hundred and seventy millions has been contracted over and above all that had been expended for the same purpose in former wars. The interest of this debt alone is not only greater than the whole extraordinary profit which it ever could be pretended was made by the monopoly of the colony trade, but than the whole value of that trade….

Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations, 1776, IV.8.53.

And the public choice part, why this persists despite the fact that the costs to Britain exceed the benefits:

To found a great empire for the sole purpose of raising up a people of customers may at first sight appear a project fit only for a nation of shopkeepers. It is, however, a project altogether unfit for a nation of shopkeepers; but extremely fit for a nation whose government is influenced by shopkeepers. Such statesmen, and such statesmen only, are capable of fancying that they will find some advantage in employing the blood and treasure of their fellow-citizens to found and maintain such an empire. Say to a shopkeeper, ‘Buy me a good estate, and I shall always buy my clothes at your shop, even though I should pay somewhat dearer than what I can have them for at other shops’; and you will not find him very forward to embrace your proposal. But should any other person buy you such an estate, the shopkeeper would be much obliged to your benefactor if he would enjoin you to buy all your clothes at his shop.

From Smith, Wealth of Nations, IV.7.149