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-ito Diminutive suffix.
From Vulgar Latin *-ittus 'id.' Of unknown origin. Variation in Vulgar Latin *-itus ~ *-ittus may parallel Aquitaine Basque *-to- ~ *-tto-. In which case we are dealing with a loan from a non-Indo-European language.
Indo-European
Romance
Asturian -etu, Portuguese -ito, Catalan -et, Occitan -et French -et, Italian -itto

"Certainty, of course, is not attainable in the study of such obscure elements of language [such as *ittus]... these phenomena, which, though not quite unnoticed, are far from having hitherto received due attention on the part of Romance scholars." ~ A. J. Carnoy, "Apophony and Rhyme Words in Vulgar Latin Onomatopoeias" (1917)

"[The suffix] -ito denotes approval/affection and is diminutive in value.... Its Latin origins are hazy; it may have been extracted from personal names (JŪLITTA, BONITTA, SALVITTUS), but must have acquired frequent use in spoken Latin, as it is well attested in Romance.... The form of the Latin suffix appears to have alternated between *-ĪTTU, whence Sp. -ito, and *-ǏTTU, from which the remaining Romance forms descend, including Fr., Occ., Cat. -et, borrowed by Castilian as -ete...." ~ R. J. Penny, A History of the Spanish Language (2002)