weakness vs preference

weakness and preference both are nouns.

Word	Noun	Adjective	Verb	Adverb
weakness	Yes	No	No	No
preference	Yes	No	No	No

As nouns, preference is a hypernym of weakness; that is, preference is a word with a broader meaning than weakness:

Other hypernyms of weakness include penchant, predilection, taste.

weakness (noun)	preference (noun)
the property of lacking physical or mental strength; liability to failure under pressure or stress or strain	grant of favor or advantage to one over another (especially to a country or countries in matters of international trade, such as levying duties)
powerlessness revealed by an inability to act	the right or chance to choose
a penchant for something even though it might not be good for you	a predisposition in favor of something
a flaw or weak point	a strong liking
the condition of being financially weak