heave up vs heft

heave up is not a noun while heft is a noun.

Word	Noun	Adjective	Verb	Adverb
heave up	No	No	Yes	No
heft	Yes	No	Yes	No

As verbs, heave up and heft are synonyms defined as:

Other synonyms of heave up include heave, heft up.

heave up (noun)	heft (noun)
	the property of being large in mass

heave up (verb)	heft (verb)
lift or elevate	lift or elevate
	test the weight of something by lifting it