There are quite a few references to Langworths, Longworths and Longworthys in early Virginia, and it will take some time time and effort to sort out their stories. Here's a first list, which I hope to enhance in future updates:

• Francis Langworth, aged 25, was transported to Virginia on the Speedwell of London on or shortly after May 28, 1635. (Tepper, Passengers to America, p.85)
  Some sources say that the Longworths who appear in Virginia Censuses after 1820 were his descendants, but I haven't seen any documentation for that claim.
• John Longworthy, 1637 (Filby, V2, p.1238)
• Jonathan Langworth, 1638 (Filby, 1984 Supplement, p.307)
  Jonathan Langworthy, "chirurgion" (probably a ship's surgeon) received land on three occasions between March 1637 and May 1638 for transporting persons to Virginia. It isn't clear that he actually settled in Virginia.
• James Longworth, 1652 (Filby, V2, p.1238)
  Edwin Connaway received land in December 1652 for transporting James and 5 others to Virginia. (Nugent, Cavaliers and Pioneers, V1, p.271)

There are also records showing that Richard Sledge and Christopher Allen were apprenticed in England to John Longworth for service in Virginia. This doesn't necessarily mean that this John Longworth resided in Virginia, because individuals in England and ship captains weren't required to live in the Virginia in order to indenture servants there.

The 1790 Census of Virginia doesn't show any heads of household named Langworthy, Langworth, Longworthy or Longworth.