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It's possible that it comes from the same origin as Darcy. In French, d'Arcy means "of Arcy". De Arze looks like the Spanish equivalent d'Arcy.

All I can tell you is that it's a Spanish surname, it's possibly locational (although I can't find a corresponding place of origin, yet), and it's old (I found 16th-century examples). I searched all the data I could find for the surname in the UK and could only find one born here, in 1835 in London, with a Spanish father; he presumably left the country later, as there's no further data for him. I think you may need to find the paternal grandparents, as it looks to me as if there's a possible link to Spain or a Spanish-speaking country.