matter vs weigh

matter is a noun but weigh is not a noun.

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

As verbs, matter and weigh are synonyms defined as:

Other synonyms of matter include count.

As verbs, weigh is a hyponym of matter; that is, weigh is a word with a more specific, narrower meaning than matter:

Other hyponyms of matter include press.

matter (noun)	weigh (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)

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