The Tallit prayer garment is symbolic of a “Chupah”, a wedding canopy. True, the children aren’t getting married quite yet! However, standing in the Synagogue by the holy Ark under a prayer garment shows the purity of the children and how beloved they are to God.
In virtually all Synagogues there exists the custom that the children are blessed in such a manner on Simchat Torah, when we celebrate and rejoice with the Torah. I have never heard of the custom to bless the children in this manner every Sabbath, but it sounds like a very beautiful custom!