Genesis 22 states from what I can gather that Milkah (daughter of Haran, niece of Abraham) married her uncle (Abraham's other brother) Nahor. She had children it appears after Abraham's (Isaac's sacrifice) Mount Moriah incident and the death of Sarah.
Do we have any clues or more information as to Abraham's age was when Rebecca was born?
Rivka was born at the time of the Akeidat Yitzchak, according to Rashi on Bereshit 25:20, based on ibid 22:20. Yitzchak was 37 at the time, based on the fact that Sarah died then, at 127 (ibid 23:1), and she was 90 when Yitzchak was born (ibid 17:17), and Avraham was 137 at the time (because Yitzchak was born when he was 100 - ibid 21:5). Yitzchak married her when he was 40 (ibid 25:20), so therefore Avraham would have been 137 when Rivka was born, according to Rashi, based on Seder Olam, which fills in some of the gaps, specifically the fact that 22:20 implies Avraham got news of Rivka's birth, and Sarah's death (implied by 23:1), both at the time of the Akeidat Yitzchak [I suspect there is no way to calculate the age based on direct scripture without this exegetical fact].
This subject has been discussed at length in the commentary to Midrash Seder Olam by R. Guggenheimer, here's a quote with some modifications for readability:
"In most French manuscripts and sources the reading (of excerpt from Seder Olam chapter 1):
Our forefather Yitzchak was 37 years old when he was bound to the altar (Bereshis 21:34)...At that time Rivka was born. It follows that Yitzchak married Rivka when she was 3 years old"
In a few (French manuscripts) we find reading "4 years". Some Oriental-Sephardic manuscripts have reading "14 years".
The reading "3 years" is quoted by Rashi on Bereshis 25:20 (see Rabbi Kaii's answer) and Tosafos Yebamos 61b (s.v. וכן), who write "Seder Olam teaches explicitly that she was 3 years old when Yitzhak married her and it is impossible to emend the text since we read there: 'Our forefather Yitzchak was 37 years of age when he was bound to the altar and at that time, 'Rivka was born' and it is written (Bereshis 25:20) 'Yitzchak was 40 years old when he married Rivka.'" Once one accepts the reading "37 years" ..., the unlikely conclusion that Rivka went out alone to fetch water at the age of 3 seems inescapablle.
The reading "4 years" can also be explained the same way: Abraham was informed of Rivka's birth on his return from Mount Moriah, so Rivka can be assumed to be born in the preceding year. This argument does not violate any of Rabbi Yose (b. Chalafta) principles (that Scripture does not come to hide but to explain). But if we accept the reading "37 years" (for Yitzchak), it seems better to accept also the reading "3 years" (for Rivka), not only because of the overriding authority of Rashi and Tosafos, who accept the reading, but also as we have seen before (in the commentary to the midrash), that R. Yose accepts the opinion of R. Yehoshua, that the years start in Nissan, and the patriarchs and matriarchs were born in Nissan. The tradition that the Akkeida on Mount Moriah was on the 1st day of Tishrei; there seems no dissent to this opinion. Therefore the messenger would have more than 6 months (to travel) from Charan to Beer Sheva. In addition, Rashi is a very careful reader of manuscripts, who never hesitates to point out readings he finds questionable.
But nevertheless it is difficult to accept the reading "3 years". The text "at that time Rivka was born" is found in all manuscripts, whether ashkenazic, Sephardic, or Oriental. The text is the base for computation "3 years" as explained. On the other hand, none of the Galilean midrashim has any trace of an opinion that Rivka married as a toddler. Also Talmud Bavli Yebamos 61b is clearly of the opinion that Rivka married as na'arah, a girl in her puberty, who legally is no longer a minor but has not yet acquired the status of an independent adult. This also seems to be implied by the legal language of the verse Bereshis 24:16. The Talmud (loc. cit.) has difficulties with reconciling the rule, derived from Bereshis 16:3, that a couple after 10 years of childless marriage is obliged to seek ways to have a child with the fact (Bereshis 25:20,26) that Yitzchak waited 20 years after his marriage before he was roused to activity. If Rivka actually was only 3 years of age, the first nine years of her marriage would not count since, for a minor, any pregnancy is a hazard to her health or life (Yebamos 12b). However, the Talmud, which otherwise follows Seder 'Olam very strictly, does not choose this easy way out but instead insists that Yitzchak was sterile during the first ten years of his marriage.
In addition, R. Yose (ben Chalafta) is quoted in Pirkei D'Rebbi Eliezer (Chapter 32) saying "3 years did Isaac mourn his mother. After 3 years he married Rebecca and forgot the mourning for his mother," without mentioning that he had to wait anyhow since 3 years is the minumum age after which a father can marry off his daughter. Similarly, the Gallilean Bereshit Rabba (57:2) mentions that "after these happenings" (Bereshis 22:20) of the 'Akkeidah, Abraham realized that he should find a mate for Yitzchak and was informed of Rivka's existence, without insisting that it was a notice of her birth. In fact, as explained ..., the notice that Abraham received from his family was a notification of his father's death, with the notices on his brother's children being incidental. Therefore, it seems clear that one should accept the reading "14 years" as the original reading of Seder 'Olam, as given in Oriental - Sephardic manuscripts.
The Tosafos themselves (Yebamos 61b) give the following argument: "Rebbi Sh'muel (ben Kalonymos) the Pious of Speyer proved that Rivka was 14 years old since it is stated in Sifri (Devarim # 357, cf. also Bereshis Rabba 100:10): 6 couples lived the same number of years, and among them Kehas (son of Levi) and Rivka. Kehas lived 133 years as given by Scripture (Shemos 6:18), and if Rivka was 14 at the time of her marriage then the computations come out right. When Yaacov was born she was then 34 years of age and Yaakov was 99 years old when his mother died (see Seder Olam Chapter 2), that makes 133 years. For Yaakov was 63 years old when he received his father's blessing (Seder 'Olam Chapter 2), 14 years he hid in the house of Ever (loc. cit., Megillah 17a), 20 years in Laban's house (Bereshis 31:38), 2 years he spent on the road (Seder 'Olam Chapter 2), and at that time Rivka died (Seder 'Olam Chapter 2), as we explain, based on Bereshis rabba 81:5, Koheles rabba 7:2, Tanchuma Teitze 4, Tanchuma Buber Vayishlah 26, Pesiqta d'Rav Kahana Zakhor 24a: "(Bereshis 35:8) allon bakhut, aλλov בכות another crying, two mournings,one for Rivka and the other one for her wet nurse (Devorah); for a total of 99 years. One has to assume there are different midrashic traditions."
We even know that not Rebbi Sh'muel the Pious is the author of the argument but Rebbi Eliezer ben Nathan of Mayence / Maynz, known as RAVa"N (Responsa, #118). He reports to have been asked by Rebbi Sh'muel ben Kalonymos about the source for the assertion that Rivka's life was equal in length to that of Kehas "and I answered him, it is taught in Seder 'Olam: At the time of the 'Akkeidah, Rivka was born and was married to Yitzchak at age 4, and Devorah the wet-nurse of Rivka died (Bereshis 35:8) together with Rivka, and if you compute from the 'Akkeidah to the death of Devorah you will find only 123 years and she would have lived 10 years less than Kehas. But certainly, the author of Sifri disagrees with the author of Seder 'Olam and in his opinion she was 10 years old at the time of the 'Akkeidah and was married at age 14, or also he might be of the opinion that she was born at the time of the 'Akkeidah but he does not accept that she died at the same time as her wet-nurse but lived another 10 years and the entire statement is a tradition (not supported by Scripture)." His interpretation is accepted by the later French commentator Chizkuni (Bereshis 25:20) as based on the correct reading of Seder 'Olam "14 years."
As explained in the introduction (of the commentary), it seems that Seder 'Olam is a Babylonian compilation of the school of Rav, based on Rebbi Yose's material. There are also good reasons to accept the attribution of the editing of Sifri to the same school. Therefore, it is most reasonable to accept the reading that Isaac was 26 years old at the time of the 'Akkeidah and Rivka was married at age 14 as the original Babylonian text. This is also the opinion of C.J. Milikowski."
To answer the question:
Opinion 1 (French manuscripts of Seder Olam Rabba according to Rashi). Rivka was born at the time of Akkeida which was also the time of Sarah's death. She was 3 years old when she married Yitzchak, who was 40 at the time of the marriage. Abraham was 137 years at the time of Akkeidah, since he was 100 when Yitzchak was born.
Opinion 2 (Oriental-Sephardic manuscripts of Seder Olam Rabba). Rivka was born at the time of Akkeida. Rivka was 14 when she married Yitzchak. Thus, she was born 11 years prior to Sarah's death. In other words, Yitzchak was 26 years old at the time of the Akkeidah and Abraham was 126 years old then. Sarah imeinu died 11 years later.
The opinion that Sarah died because of the Akkeidah comes from a later Rabbi Yose (Bereshis Rabba 58:5). There is a manuscript of Seder Olam stating that "Our father Yitzchak was 26 years old when he was bound to the altar." This reading was also proposed by the Vilna Gaon.
Opinion 3. Sifri Devarim as explained by Rebbi Eliezer ben Nathan of Mayence and Rebbi Sh'muel (ben Kalonymos) the Pious of Speyer. Rivka was born 11 years prior to the time of Akkeida, which also was the time of Sarah's death. Rivka was 14 when she married Yitzchak, who was 40 at the time of the marriage. Abraham was 137 years at the time of Akkeidah, since he was 100 when Yitzchak was born. Thus, he was 126 years old when Rivka was born.
I also heard that there could be a reconciliation between all these opinions based on mysticism (most likely source Or haChaim, but I did not see it there). As we know, Sarah, mother of Yitzchak died 3 years prior to Rivka's marriage. Perhaps, a part of Sarah's soul at that time was given to Rivkah. Thus, one can say that as Rivkalah, daughter of Bethuel haArami, she was 14 when she married Yitzchak. However, as a girl with potential of Rivka imeinu she was only 3 or 4 years.
