heft vs heave up

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

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

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

Other synonyms of heft include heave, heft up.

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

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