What does the Medrash mean when it tells us that Rivka was three years old when she married Yitzchok? Is that meant in a literal sense? If so, how is this to be explained in a rational way?
The following I remember from a Sicha of the Lubavitcher Rebbe:
Rashi at the end of Parshas VaYeira feels the need to explain why the "news" Abraham received about his family tree is written right after the Akeidah (or at all) ? He answers by showing the Medrash which states that once Issac went through the Akeidah, (at age 37) he was ready to marry, so the Torah announces Rivkah's birth (she is on the list received by Abraham). Since we know Issac married when he was 40, therefore Rivkah is 3 years old at her marriage.
Tosfos to Yevamos 61b, brings an opposing Medrash which says she was married at age 14. (see Seder Olam Rabbah)
The Rebbe (and other scholars) are bothered by the fact that the Torah calls Rivkah a "naarah" when Eliezer meets her. A naarah in Torah language can only be an older girl above 12 years of age. Otherwise, the Torah would use the word "katanah" if she were really physically 3.
Based on this apparent contradiction, the Rebbe resolves it by saying the Seder Olam age of 14 is her physical age. The Medrash brought by Rashi, is not speaking physically, but spiritually. We know that Sarah passed away exactly at the time of the Akeidah. The Tanya explains that according to Kabbalah, a righteous person who dies, may sometimes be granted a mission to help a struggling living person in this world. The Tzadik/Tzadekes who passed has their soul reborn into the soul of their "student" on Earth, in order to help them overcome spiritual obstacles. This is called the secret of "Ibur Neshamah".
Sarah was reborn into the soul of Rivkah at the Akeidah (right after Sarah's passing). Therefore, the Medrash calls her a "three year old" at her wedding. That is, three years since she was born with Sarah's soul (which happened when she was physically 11).
Further proof that we are dealing with a living shared incarnation, is that Rivkah's arrival causes the return of Sarah's blessings (cloud, lights, dough). Issac is consoled "after his mother" and "brings her to his mother's tent" specifically. (Gen. 24:67)
In addition, I say that the "news" Abraham receives could not possibly have happened all at once. It is a long family tree with the report of many births over a long time. There is no reason to say Rivkah, who is on the list, was born exactly then (at the Akeidah when the news was sent) unless we are speaking of a spiritual birth.
So, Rivkah was 14 when she married Issac. She was 3 years old as a combined soul with Sarah.
The problem many people have with this IMHO, is that they only know the Rashi (not Tosfos and other meforshim) and take Rashi very literally on his use of a Medrash. But Medrashim were not usually meant to be used literally!
Therefore they find themselves stuck choosing between defending their faith (she was 3) and facing rational objection (how did she do the camel marathon...child marriage etc.)
The fact is, its just not a problem.
Yes, there were cases of ancients who were physically stronger and more mature at younger ages. The Gemara does show this to be the case. However, it does not seem to be so regarding Rivkah Imeinu.
Rav Schwab, in his sefer "Meiyun Beis Hashoeva", explains Rivka being 14.5 using a similar approach to that of Lubavitcher Rebbe mentioned above.
An English summary of the approach can be found at: http://www.nachumsegal.com/taking-closer-look-parshas-toldos-rabbi-dov-kramer-5774/