Chabad.org — English translation + Rashi
Torah Temimah (Shabbos 130a): “בכה למשפחותיו” — they wept over the matters of their families (the newly forbidden arayos), as linked to the reading of “dagah” above.
English: “Weeping by their families” — over the affairs of their families: the forbidden relations that had been closed to them.
Family weeping — the midrash ties the tears at the tent openings to the sexual prohibitions, not only to meat.
The public cry is read as a protest against the new boundaries of kinship.