What kind of love does the poet want?
The speaker of the poem wants her lover to love her for the sake of love itself. The speaker is very clear that she does not want to be loved because she has a great smile or because she had a nice voice. The speaker is very clear that she shouldn't be loved for any kind of surface level visual or auditory reason.
Do not say, “I love her for her smile—her look—her way Of speaking gently,
Shakespeare would be proud of such thoughts by the way. His Sonnet 141 is all about how his eyes and ears can't stand the sight and sound of his lover, yet he still loves her deeply.
"In faith, I do not love thee with mine eyes,
For they in thee a thousand errors note; . . .
Nor are mine ears with thy tongue's tune delighted,"
He loves her for the sake of love, which is exactly what Elizabeth Barrett Browning is saying in her Sonnet 14. The speaker in Browning's poem doesn't want to be loved for any of those surface reasons, because those things can, and do, change over the course of time. She wants to be loved for the sake of love, which in her opinion is a sign that the love will remain unchanged for eternity.
But love me for love’s sake, that evermore Thou mayst love on, through love’s eternity.
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