The early Nonconformists were essentially Calvinists and this does not argue for much tolerance. Calvin's influence on the development of European Capitalism is well known. His doctrine of Absolute Predestination was flattering to those who exploited others, as was his division of Christians into the Elect and the Reprobate, based on a very lawyerly interpretation of the Biblical narrative of Jacob and Esau. However my field is Irish Literature, not religious history!
In 1624, the Virginia Company's charter was revoked by King James I, and was transferred to royal authority as a crown colony
Given that Toleration to Non Anglicans wasn’t granted in Britain Until 1689, it is not surprising to see that Quakers and Baptist’s particularly might fall foul to the colony’s authorities. Surviving evidence from such targeted groups suggests that it was not as harsh as some of the New England colonies though
Toleration of "dissenters" (which is what Quakers, Baptists, semi-Calvinist Presbyterians, the demi-Calvinists in Puritan New England, and, increasingly, the Methodists by the end of the 18th century were to the official "Church of England," the Anglican church, back home in England) in a Southern colony like Virginia was a function above all of institutional weakness: the Church of England found it difficult to replicate the mother country's parish system and church hierarchy all the way on the other side of the Atlantic Ocean. After the 1740s, though, the "Great Awakening" stirred up religious feelings across all the colonies and the number of Baptists, Presbyterians, and Methodists began to grow in the Southern colonies. In Virginia one sign of the new religiosity was, ironically, a movement to create an established church in the newly independent state, a movement led by Patrick Henry, one of the most eloquent voices for revolution in the first half of the 1770s. Luckily the project was blocked by a coalition of Enlightenment-oriented friends of religious liberty like Thomas Jefferson, who authored the Virginia Statute for Religious Freedom (one of three things he wanted on his tombstone, along with writing the Declaration of Independence and founding the University of Virginia -- just being U.S. President didn't rate as highly), and James Madison, who shepherded it through the Virginia legislature while Jefferson was away as U.S. ambassador to France, together with support from Baptists, Presbyterians, and Methodists who didn't want any more oversight over their religious beliefs by an established church.
If you want to learn particulars regarding treatment of Quakers, you should be able to locate letters and minutes from their “meetings”. I have seen documents of Quakers in VA, but mostly studied those in NC - many fled there due to persecution in Va. Guilford College, NC (Quaker College) has an archive you might wish to check out.