sickliness vs infirmity

sickliness and infirmity both are nouns.

Word	Noun	Adjective	Verb	Adverb
sickliness	Yes	No	No	No
infirmity	Yes	No	No	No

As nouns, infirmity is a hypernym of sickliness; that is, infirmity is a word with a broader meaning than sickliness:

sickliness: The state or characteristic of weakness, incapacity, or physical distress due to poor health, especially of a chronic nature.
infirmity: the state of being weak in health or body (especially from old age)

Other hypernyms of sickliness include debility, feebleness, frailness, frailty, valetudinarianism.

sickliness (noun)	infirmity (noun)
The state or characteristic of weakness, incapacity, or physical distress due to poor health, especially of a chronic nature.	the state of being weak in health or body (especially from old age)