I have been trying to e-mail Pedro J. Aguiar formerly of this site but the addresses are bad. Anyone have a current e-mail for him?
My own branch of the Aguiar family came to Hawaii in the late 1800s under the name de Aguiar and from Madeira. The family says that the family was, of course, from Portugal originally, but also was of Basque origin. I have seen nothing here on the Basque aspects of the family name. Basques that I know seem to claim de Aguiar as one of their names.
Also, a text I have on Sephardic Portuguese history points out the town of Aguiar as one of the active Portuguese Jewish communities prior to the expulsion from Spain and Portugual in the late 15th century. Apparently Madeira was one port of refuge for them in those days, but undoubtedly there were many others.