Something to do with a sigh? (5)

I believe the answer is:

heave

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'a sigh?' is the definition.
(thesaurus)

I don't understand how the remainder of the clue works.

(Other definitions for heave that I've seen before include "Pitch" , "Lift or throw with great effort" , "Produce (a sigh); retch" , "Pull hard; (sea) swell" , "gag" .)

I've seen this clue in the Evening Standard.

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