Why do all subjects in Tudor paintings appear to look similar and have dark eyes?

It could be one of at least two things:

1. That was the fashion of the time. You had yourself painted the way you wanted to be painted. And you wanted to be painted as better looking than you really were. Maybe people thought dark eyes looked good.
2. Subjects of Tudor paintings were of members of Aristocratic families. In those days, rich people only married rich people, and the bloodlines all got mixed. This led to a fair amount of inbreeding. People are bound to look similar.