What kind of society did Berkeley envision for Virginia?
First, Lord Berkeley was most closely associated with New Jersey, not Virginia.
Lord John Berkeley was first granted land in the colony of New Jersey thanks to his relationship with Charles II and The Duke of York. He was also granted some lesser land titles in the Carolinas, but was a co-proprietor of the New Jersey colony for about ten years. As such, he had an immense say in the formation of the colonies laws and tenets, and was instrumental in drafting what became known as the Concession and Agreement. This document, which was written in 1665, lays out the structure of the colonial government, but also grants religious freedom inside the colony. This declaration, which was unusual for its time, was part of Berkeley’s vision for the new colony. He had been exiled after the English Civil War and forced to live in Paris until the restoration, so he knew well what it was like to be the target of religious persecution. For this reason, he wanted to make sure that New Jersey was free from such tumultuousness and penned this important charter of religious freedom. He knew that if religious tolerance were granted, more people would flock to the colony and his profits would increase. The success was short lived, mostly due to differences of opinion between himself and the governors of neighboring colonies, which eventually led to New Jersey being seized by the crown in 1702 when it began to incur too much debt.
The question is referring to William Berkeley, not John Berkeley. William Berkeley was governor of Virginia both before the English Civil War and after the Restoration. He was a very significant figure, perhaps more so than John Berkeley. He envisioned Virginia as an elite-controlled oligarchy governed with a minimum of popular consent. He used powers of patronage to cultivate alliances with the developing gentry in Virginia (indeed he did much to help that gentry to develop in the first place.) In particular, he gave valuable grants of land to favorites, who then sold them on to speculators. He also allowed the gentry to monopolize the fur trade with Native Americans. After being restored to the governor's office with the Stuart restoration, he refused to hold new elections to the Virginia Assembly, allowing only his cronies to remain in power. They in turn levied heavy taxes on smallholders in Virginia. In 1676, popular anger at Berkeley and the opulent planter class he represented came to a head with Bacon's Rebellion, an uprising led ironically by a former friend of the governor's. While the immediate cause was related to fighting with Susquehannock Indians on the frontier, the roots of the conflict extended to the immense inequalities and economic injustices that Berkeley had perpetrated.