To my knowledge the system worked similarly to how it works today. Business owners with very large economic bases had inherit influence within the political system of the colonies, and as an extension could influence some of the decisions made by the British parliament.

As well as this a large part of the tax revenue made by the Thirteen Colonies at the time came from the cotton trade thus the owners of the cotton plantations were mostly left to their own devices as long as they kept the revenue coming in.