Source Of The Minhag

On Shabbos a Jew attains the status of "the Shechina emanates from his mouth" and it is a mitzvah to sing Hashem's praises with our zemiros. Incidentally, this is the source of the minhag for parents to bless their children on Friday night. For on Shabbos, the Shechina speaks through the mouth of a Jew, so it is really the Shechina that is blessing the children.

(Rebbe Menachem Mendel of Rimanov)