Will they not believe my sighs
Rather than my barren eyes,
As, when laments the dove,
They say, 'He sings of love'?
Is it a metaphorical use for:
- Lacking vegetation, especially useful vegetation: barren tundra.
Because it synonymous to "empty", but it's meaningless here unless it's used as a metaphor.
"Barren eyes" is not a special well-known phrase or idiom - the words mean what they say, but figuratively since the context is artistic--poems are a work of art by definition.
Eyes are considered the window to the soul/spirit, and "empty eyes" would mean one's eyes look like they are drained of soul or spirit. The fact that "barren" also is often used to talk about a piece of land's inability to grow vegetation is likely an additional meaning leveraged in the metaphor - i.e. "the eyes look like nothing positive can grow within."
Looking at the meanings of words in poems in this level of detail is an interesting way to fully understand a poem and appreciate the depth of the impression that the writer was trying to create.
The previous verse says If my tears desert me, so presumably his 'barren eyes' are unable to weep.
The title of this poem is "Love's Evidence", and the stanza that precedes this quote is:
If my tears desert me, why
Do they slyly wink, and cry
'He has consoled him', or
'He did not love before'?
The author's eyes are "barren" in the sense that they do not produce tears. He complains that others take his lack of tears as evidence of a lack of love.
