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It's a Basque name. In U.S., predominantly found in New Mexico and Colorado. There's an Archuleta County in Colorado. "eta" means place/home of. I believe the original spelling was Arechuleta.

This surname has a spanish-bask origin. It coul come from a name of a place like many bask surnames.

This is a Basque surname and from a place name. I don't know the meaning but I've found two completely different explanations
i) "little grottoes"
ii)"place of oak trees"
As I believe that -eta is a place name ending rather than a diminutive ending I incline towards the second explanation, but as I know nothing of the Basque language my opinion is worthless.