How did the invention of white people serve to unify the relatively few plantation owners with large numbers of British and European laborers despite their dramatically different economic and social conditions?

While persons with lighter skin pigmentation have been known for thousands of years, the racial category of "white people," many scholars agree, did not originate until the seventeenth-century. It was first used in a statute enacted by the legislature of colonial Maryland in 1681 and by other colonies thereafter. Prior to this time, there was largely a level of legal and social equality between people of different skin tones. Free laborers of both African and British descent worked alongside one another on colonial American plantations.
With the recognition of different races, however, came a new separation of social and judicial standards and treatment. This helped justify the colonization of the continent of Africa as well as the creation of the institution of slavery. By creating categories of free and slave labor which were based on classes originating in the artificial distinction of skin tone, the former unity of landless British and landless African labor against wealthy landowners was broken. Instead of the landless against the landed, landless whites were united with landed whites against landless blacks. This served the interest of plantation owners by weakening an endemic threat; a threat that—in 1676—manifested itself as armed insurrection during Bacon's Rebellion.
In the podcast interview linked below, Jacqueline Battalora—a sociologist at Saint Xavier University and one of the foremost scholars on "white invention"—discusses her book Birth of a White Nation (2013), which explores these themes in depth.