It is possible that Moore's choice was inspired by the release date of Fantastic Four #1, which is considered by most to be the date the modern Marvel Universe was launched. Although the cover date of the comic book is given as November 1961, there are claims that the comic book was released as early as June 1961, hence, "61/6".
Other Alternate Earths.
It is also possible that "616" is a reference to the Number of the Beast in the final chapter of the Christian Bible, the Book of Revelation (or the Apocalypse of John). While most early manuscripts give the Number of the Beast as "666", the earliest existing fragment of the Greek text of this book gives it as "616". Irenaeus argued against the "616" number in his neverending battle against early heresies. Moore, a student of mystic esoterica from a very early age, could well have known about this alternate rendering. Quite why the Marvel Universe should even be named after the Number of the Beast may be an indirect reference to set it apart from the DC Universe. For many years, the headquarters of DC Comics was located at 666 Fifth Avenue in New York City. Thus, the name could be a subtle joke that the DC Universe was Earth-666 while the Marvel Universe was Earth-616; both numbers, of course, are renderings of the Number of the Beast.