Most likely inherited from Latin -āticus. Doublet of -aggio, from Old Occitan or Old French.
This suffix was traditionally seen as a borrowing from Latin, as it was believed that -āticus would be expected to develop into *-acco via syncope of the post-tonic vowel (such as in freddo < frigidus); furthermore, most words formed with this suffix are learned terms, such as problematico (← problēmaticus).
However, the claim that *-acco is the regular reflex of -āticus is unwarranted; Fleischman (citing E. L. Dawson) notes that "a thorough examination of Medieval Latin and Italian texts has not only failed to produce a single example in *-acco, but also discovered none showing syncope of the posttonic vowel between a dental and a velar". She also adduces a solid core of non-learned formations using -atico, such as lugliatico (< Medieval Latin iūliāticus).
-atico (adjective-forming suffix, feminine -atica, masculine plural -atici, feminine plural -atiche)
-āticō