bear upon vs influence

bear upon is not a noun while influence is a noun.

Word	Noun	Adjective	Verb	Adverb
bear upon	No	No	Yes	No
influence	Yes	No	Yes	No

As verbs, influence is a hyponym of bear upon; that is, influence is a word with a more specific, narrower meaning than bear upon:

bear upon (noun)	influence (noun)
	causing something without any direct or apparent effort
	a power to affect persons or events especially power based on prestige etc
	a cognitive factor that tends to have an effect on what you do
	one having power to influence another
	the effect of one thing (or person) on another

bear upon (verb)	influence (verb)
have an effect upon	shape or influence; give direction to
	induce into action by using one's charm
	have and exert influence or effect