The only free and comprehensive online etymological dictionary of the Spanish language
aya f. (Noun) "governess"
15th cent. From Latin avia "grandmother." From Proto-Italic *awīā 'id.' From Proto-Indo-European *h2eu̯-i̯h2- 'id.' From *h2eu̯h2- "grandparent" (see also ayo).
Portuguese aia, Catalan aia
Ancient Greek αἶα (?) (aía) "grandmother"

In the masculine, Latin avus "grandfather" took a different sense. See ayo.

The -i- in avia is a relic from a devi-type inflection in Proto-Indo-European, vanishingly rare in the Italic language family.