heaviness vs unhappiness

heaviness and unhappiness both are nouns.

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

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

Other hypernyms of heaviness include sadness.

heaviness (noun)	unhappiness (noun)
the property of being comparatively great in weight	emotions experienced when not in a state of well-being
used of a line or mark	state characterized by emotions ranging from mild discontentment to deep grief
unwelcome burdensome difficulty
an oppressive quality that is laborious and solemn and lacks grace or fluency
persisting sadness