"short-sightedness," 1727, medical Latin, from Late Greek myōpia "near-sightedness," from myōps "near-sighted," literally "closing the eyes, blinking," on the notion of "squinting, contracting the eyes" (as near-sighted people do), from myein "to shut" (see mute (adj.)) + ōps (genitive ōpos) "eye" (from PIE root *okw- "to see"). By coincidence the name describes the problem: the parallel rays of light are brought to a focus before they reach the retina.
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.