We know enough about Anthony West to be reasonably certain he had no connection with the de la Warr family. He came over as an indentured servant, served out his time, went back to England, became a chirurgeon (doctor/surgeon), married in England, and re-emigrated to Virginia with his family.
None of that even hints at anything but yeomanry or, at most, impoverished untitled gentry.
He had one known surviving son, who was *not* the same person as Col. John West of New Kent County (humongous Chesapeake Bay lies between them), and that son had a bunch of sons, allowing for testing on multiple lines.