Quick search of the 1630s produced this much on the name Stephen Hopkins... (not sure it's the same guy.)
1632/33 Legal council in Plymouth (not Virginia)
January 11 (January 1 Julian Calendar, Tuesday), New England: In Plymouth Colony, Edward Winslow defeats William Bradford in elections for colonial governor, the first time the leadership has changed for 12 years. Bradford also obtains enough votes to obtain a seat on the Court of Assistants, along with Captain Myles Standish, John Howland, John Alden, John Doane (age 42), Stephen Hopkins, and William Gilson (who serves as legal counselor for the colony). Former colonial leader Isaac Allerton is now the richest man in Plymouth Colony, but the debt he had left behind after being dismissed from the colonial government remains unpaid for the next 15 years.
1633/34 Still in Plymouth
January 11 (January 1 Julian Calendar, Wednesday), New England: In Plymouth Colony, Thomas Prence defeats Edward Winslow in elections as Plymouth’s fourth colonial governor. Winslow garners enough votes to obtain one of the Assistant positions for the year. Other Assistants include William Bradford, Isaac Allerton, John Alden, John Howland, and Stephen Hopkins.
(I guess they voted on Jan 1 in Plymouth)
1636 Still in Plymouth, having a good time
June 17 (June 7 Julian Calendar, Tuesday), New England: In Plymouth Colony, Eleanor Billington, the Catholic widow of John Billington, the first man convicted of a capital crime in British America, says in court, when questioned about overuse of a shared hay ground in a nearby marsh, that “what is too much for her is for Mr. Doane.” This prompts a suit of slander by her neighbor and fellow hay ground user Anglican Deacon John Doane (age 45), who seeks 100 pounds in damages from her in the General Court under Governor Edward Winslow. The court agrees that she had defamed him, but regards his request for damages to be way too high. Instead, the Widow Billington is ordered to pay 5 pounds and subject herself to being “set in the stocks and whipped”. (Assistant John Howland serves on the jury.) Two years later, she will remarry to Gregory Armstrong, allowing her the chance to raise her two boys in a proper family. Also convicted is Stephen Hopkins, who was accused by John Tisdale of battery; he is fined 5 pounds to His Majesty’s government for breaking the peace, and forced to award 40 shillings to Tisdale as damages.
November 1 (October 22 Julian Calendar, Saturday), New England: In the morning, Sachem Miantonomo, two sons of Sachem Canonicus and Massachusetts Bay Governor Henry Vane the Younger sign a treaty of alliance against the Pequot. As an ally, Sachem Miantonomo asks the English to spare the women and children of the Pequot in the coming campaign before leaving Boston around dinner time. (In return for Williams’ assistance, Plymouth Colony Governor Edward Winslow contributes a gold coin to the finances of Providence Colony.) Because of their ties to the Narragansett, Sachem Massasoit (Ousamequin, age 55) keeps the Wampanoag Confederation from supporting the Pequot, remaining neutral in the coming war, in deference to his friendship with John Carver, Stephen Hopkins, Edward Winslow, William Bradford, and Captain Myles Standish. (“The English are my friends and love me. Whilst I live, I will never forget the kindness they have showed me.”)
1637 Still in Plymouth, Johny-come-lately in the War with the Pequot
June 17 (June 7 Julian Calendar, Wednesday), at a General Court, Governor William Bradford reverses the decision of his predecessor, Edward Winslow, and agrees to “send forth and assist them of Massachusetts Bay and Connecticut in their wars against the Pequot Indians, in revenge of the innocent blood of the English which said Pequot have barbarously shed, and refuse to give satisfaction for.” Stephen Hopkins and John Winslow are appointed to gather men for an army from the town of New Plymouth, John Howland and Jonathan Brewster are appointed to gather men from “Duxburrow” (Duxbury), and Gilson and Edward Forster are appointed to gather men from Scituate. A sum of 200 pounds is raised to pay the men before it becomes known that the men are no longer needed (the war had already been won before they even begin to march toward the Connecticut River valley). Other business includes declaring Duxbury a township, and determining how to restore strength in the fur trade after fur-rich areas begin to decline.
And an Edward Hopkins figures pretty large in the next decade in Connecticut politics.