Maqam Bayat is a slumber sounding maqam and does not necessarily imply a given theme. It is the most commonly used of the Syrian Maqamot. More songs in the pizmonim book are classified under this maqam than any other. This maqam has a mellow mood to it and therefore is used for Arbit Mossae Shabbat and Mossae Yom Tov when the mood of ending the day is such.
Bayat symbolizes an oath between two parties (as is the case with Bar Mitzvah- an oath between man and God). Bayat is associated with the occasion of a Bar Mitzvah due to its wealth of Bar Mitzvah pizmonim. It is also used on Mossaei Shabbat due to its wealth of Mossaei Shabbat pizmonim. Bayat is used for both the celebrations of baby girls and the Bar Mitzvah. A possible explanation for this is that daughter in Hebrew is BAT, which sounds somewhat similar to Bayat.