weigh vs matter

weigh is not a noun while matter is a noun.

Word	Noun	Adjective	Verb	Adverb
weigh	No	No	Yes	No
matter	Yes	No	Yes	No

As verbs, weigh and matter are synonyms defined as:

Other synonyms of weigh include count.

As verbs, matter is a hypernym of weigh; that is, matter is a word with a broader meaning than weigh:

Other hypernyms of weigh include count, weigh.

weigh (noun)	matter (noun)
	that which has mass and occupies space
	(used with negation) having consequence
	some situation or event that is thought about
	a vaguely specified concern
	a problem
	written works (especially in books or magazines)

weigh (verb)	matter (verb)
show consideration for; take into account	have weight; have import, carry weight
determine the weight of
have a certain weight
have weight; have import, carry weight
to be oppressive or burdensome