Hisham narrates from his father, and he from Sayyidah Aishah (may Allah be pleased with her), that Barirah made a contract (mukatabah) for her freedom for 9 uqiyahs, one uqiyah to be paid each year. She came to Sayyidah Aishah (may Allah be pleased with her) seeking her help, and Sayyidah Aishah (may Allah be pleased with her) said: If they wish, I will pay the price all at once, and the wala' will be mine. Barirah went and spoke to her people; they refused, except on the condition that the wala' be theirs. Barirah came to Sayyidah Aishah (may Allah be pleased with her), and the Messenger of Allah (peace and blessings be upon him) also came there. Barirah came and told Sayyidah Aishah (may Allah be pleased with her) what they had said, and Sayyidah Aishah (may Allah be pleased with her) said: This is only possible if the wala' is mine. The Messenger of Allah (peace and blessings be upon him) said: "Buy her, stipulate the wala' (for them), and set her free, for the wala' belongs to the one who sets free." Then he (peace and blessings be upon him) addressed the people; he praised and extolled Allah and said: "What is wrong with people who stipulate conditions that are not in the Book of Allah? They say: 'O so-and-so, set (him) free, and the wala' will be mine.' The Book of Allah is more truthful, the conditions of Allah are more reliable, and any condition that is not in the Book of Allah is void, even if it be a hundred conditions." Sayyidah Aishah (may Allah be pleased with her) said: The Messenger of Allah (peace and blessings be upon him) gave Barirah the choice regarding her husband. Her husband was a slave, so Barirah chose herself (that is, she separated from him). Urwah said: If he had been free, the Prophet (peace and blessings be upon him) would not have given Barirah the choice.
(b) The narration of Ishaq bin Ibrahim is in (Sahih) Muslim. It contains the evidence we intended, and (shows) that the wala' belongs only to the one who sets free, not to anyone else. Among the rulings of wala' is that guardianship in marriage is also established (for the holder of the wala') when no related guardian exists.
There are other hadiths too regarding the consideration of kafa'ah (equality in marriage), but it is not correct to take them as proof. (And Allah knows best.)
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 13756