eyesight vs sight

eyesight and sight both are nouns.

Word	Noun	Adjective	Verb	Adverb
eyesight	Yes	No	No	No
sight	Yes	No	Yes	No

As nouns, sight is a hypernym of eyesight; that is, sight is a word with a broader meaning than eyesight:

Other hypernyms of eyesight include vision, visual modality, visual sense.

eyesight (noun)	sight (noun)
normal use of the faculty of vision	the act of looking or seeing or observing
	the ability to see; the visual faculty
	an instance of visual perception
	the range of vision
	a range of mental vision
	a place of interest, especially to visitors
	anything that is seen
	(often followed by `of') a large number or amount or extent

eyesight (verb)	sight (verb)
	catch sight of; to perceive with the eyes
	take aim by looking through the sights of a gun (or other device)