"Heave up" is a phrasal verb that means "to lift something with effort or force". There are several synonyms for this verb that convey a similar meaning. One such synonym is "hoist", which also means to lift something upwards with force. "Elevate" is another synonym that means to raise something to a higher position or level. "Lift" and "boost" are also effective synonyms for "heave up". "Pull up" and "yank up" are standard synonyms that suggest an action that requires effort and strength. In conclusion, Synonyms for "heave up" include hoist, elevate, lift, boost, pull up, and yank up, among others.