mid-15c., from Late Latin folio "leaf or sheet of paper," from Latin folio, ablative of folium "leaf" (source also of Italian foglia, French feuille, Spanish hoja), from PIE *bhol-yo- "leaf" (source also of Greek phyllon "leaf," Gaelic bile "leaflet, blossom"), suffixed form of root *bhel- (3) "to thrive, bloom." Ablative of location, because this was used in page references. Meaning "volume of the largest size" first attested 1620s.
Middle English -ik, -ick, word-forming element making adjectives, "having to do with, having the nature of, being, made of, caused by, similar to," from French -ique and directly from Latin -icus or from cognate Greek -ikos "in the manner of; pertaining to." From PIE adjective suffix *-(i)ko, which also yielded Slavic -isku, adjectival suffix indicating origin, the source of the -sky (Russian -skii) in many surnames. In chemistry, indicating a higher valence than names in -ous (first in benzoic, 1791).
In Middle English and after often spelled -ick, -ike, -ique. Variant forms in -ick (critick, ethick) were common in early Modern English and survived in English dictionaries into early 19c. This spelling was supported by Johnson but opposed by Webster, who prevailed.