tearfulness vs unhappiness

tearfulness and unhappiness both are nouns.

Word	Noun	Adjective	Verb	Adverb
tearfulness	Yes	No	No	No
unhappiness	Yes	No	No	No

As nouns, unhappiness is a hypernym of tearfulness; that is, unhappiness is a word with a broader meaning than tearfulness:

Other hypernyms of tearfulness include sadness.

tearfulness (noun)	unhappiness (noun)
sadness expressed by weeping	emotions experienced when not in a state of well-being
	state characterized by emotions ranging from mild discontentment to deep grief