You are correct in that the answer is connected with the Approbations.
Rabbi Weiner is a recognized G-d Fearing Torah Scholar in serious Rabbinic circles, and as such he did not undertake this significant work on his own authority. Each step of the way, in his four years of dedicated work and exceptionally thorough research on the two volumes of "Sheva Mitzvot HaShem" ("Seven Divine Commandments") in Torah-Law Hebrew, he consulted and sought the approval of outstanding Halachic authorities, as explained on this web page:
http://www.judaism.com/display.asp?etn=CDGCD
His work was fully reviewed in detail, and annotated in the printed version, by one of the Chief Justices of the Supreme Rabbinical Court of Israel, Rav Zalman Nechemiah Goldberg. Rav Z.N. Goldberg is universally recognized as one of the outstanding Torah scholars of our generation. (He is also the son-in-law of one of the greatest Torah Authorities of our Generation, Rav Shlomo Zalman Auerbach.)
"Sheva Mitzvot HaShem" has the approbations of both the Ashkenazic and Sefardic Chief Rabbis of Israel, Rav Metzger and Rav Amar, respectively. You can read their translated letters in full at the top of this page:
http://www.asknoah.org/RecommendedBooks.html
To view the original letters:
http://www.asknoah.org/Rabbi_Amar_letter...essing.pdf
http://www.asknoah.org/Rabbi_Metzger_let...essing.pdf
This work also received glowing approbations from Rav Gedalia Dov Schwartz, the Head of the Beis Din (Rabbinical Court) of the Rabbinical Council of America and the Rabbinical Council of Chicago. Rav J. Immanuel Schochet, who is a prominent Torah Scholar and a prolific author of fundamental Torah texts, in Toronto, Canada, also participated in the project, and contributed a great deal to the section in Volume 1 on recommended prayers for righteous Gentiles, and most of the Section Introductions in "The Divine Code."
In the Introduction to his work, Rabbi Weiner clearly explains the fundamental principles for understanding and codifying the practical applications of the Noahide Mitzvot, including the main (but not sole) authority in this area of Torah that is accorded to the teachings of "Rambam," Rabbi Moses Maimonides. Rabbi Weiner also drew much inspiration from the homiletics on the Noahide Mitzvot in the classic book "Mitzvos Hashem" by Rabbi Yonasan Shteif, who was the Chief Rabbi of Vienna, Austria, before WWll.
For the Gentile world, the book series "The Divine Code" is the English translation approved by Rabbi Weiner, with editorial notes, of "Sheva Mitzvot HaShem":
http://www.judaism.com/display.asp?etn=CDGCG
This English volume has been presented to and found praiseworthy by several English-speaking Chassidic Rebbes, and one of the Justices of the Rabbinic Court of the Eidah HaChareidis of Jerusalem. "Sheva Mitzvot HaShem" and "The Divine Code" are published by Ask Noah International, and can also be obtained directly through this web site.
Seldom do you find such unanimous approval from so many various groups and segments within the branches of Traditional Torah Judaism. All of this is what sets "Sheva Mitzvot HaShem" and "The Divine Code" apart from any other books that have ever been written about the practical Torah-Law applications of the Noahide Code.
In these books, Rabbi Weiner explains where some contemporary Rabbis have given opinions that are more stringent than necessary on some aspects of observance (and note that righteous Gentiles may *voluntarily* choose to follow extra stringency in some areas if they wish), while in some other aspects, opinions have been given that are overly lenient (including in some matters that involve cross-over into uniquely Jewish Mitzvot, or that are contrary to the general obligation that Gentiles have for acting in accordance with "yishuv olom" - establishing, and not detracting from, the Torah's ideals for settled, orderly and law-abiding societies for the world's inhabitants).
In any event, everything is footnoted for those who want to look into the Torah-based sources in more depth.