Hat at kidush

The minhag in Ashkenaz was to keep the hat on for Kidush (since it was on at shul, it's not the right honor for the mitzvah of kidush to take the hat off for it), but one was not required to put it back on for Bircas Hamazon. Wearing a hat is considered a more important way to be dressed up (it's considered special shul clothes), and therefore it's should be worn on Kiddush, rather than just having the kippah on (but there was no importance to a double head covering in Ashkenaz, only by the Chassidim).
The same logic was used with the tallis in mincha of Shabbos - whoever gets an Aliyah for Mincha does not take it off until Kedushah, because it is not honor for the Amidah and Kedoshoh to take the tallis off before them (even though whoever doesn't have a tallis on does not put it on for Amidah of Shabbos).

Michael FRBSH