1
general::
In a sad or miserable state, unhappily, as in He left her with a heavy heart, wondering if she would ever recover. The adjective heavy has been used in the sense of "weighed down with grief or sadness" since about 1300. Its antonym light dates from the same period. The latter use survives only in light heart, meaning "freedom from the weight of sorrow"? that is, "a happy feeling." For example, She left for Europe with a light heart, knowing that the kids would be fine.
American Heritage Idioms
2
general::
Phrase(s): with a heavy heart
Cliché sadly. • With a heavy heart, she said good-bye. • We left our summer cottage on the last day with a heavy heart.
McGrawhill's American Idioms And Phrasal Verbs