Answer:
Sadness and a broken heart
Explanation:
In "When I Was One-and-Twenty," by A.E. Housman, the connotation that the poet uses for the word in bold (sighs) is sadness and a broken heart. In the first part of the poem, a wise man is advising the twenty-one-year-old poet. This wise man told him to give valuable gifts as precious stones, and money, but not to give away his heart. The poet now aged twenty-two has not followed this advice and is paying with sorrow, sadness, and regret.