The speaker in Elizabeth Barrett Browning's sonnet wants her beloved to love her for her soul, not for outward physical reasons. She says the outward reasons for love can go away. In that case, a love based on superficial or shallow elements can quickly disappear.
Her beloved says he loves her for her physical appearance, such as her smile and her "gentle speech." However, she tells him, those aspects of her might change. Would he then stop loving her? He also tells her he loves to pity her and wipe her tears away. She notes, however, that if they stay in love, his love will cure her of feeling sad. Would her happiness drive him away?
Instead, she wants her beloved to love her "for love's sake." She wants an "eternal" love based on a deep connection, not a weak love based on her external traits.