heavy heart, with a - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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 wit 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.