The reason is linked with the Shabbat hymn, L’cha Dodi. The hymn calls upon the Beloved to join in welcoming the Shabbat Bride.
The link is not merely that both focus on the word dodi, “My Beloved”. It goes deeper.
If taken allegorically, the sometimes daring imagery of Shir HaShirim depicts the yearning of the spirit for the ecstasy of spiritual union – with Shabbat, with the Torah, with the Land of Israel, with God Himself.
In the M’chilta, Rabbi Akiva says, “I speak of the beauty and praise of God before all the nations”. They ask Israel, “What is your Beloved more than any other beloved one?” An answer is given in Midrash Shir HaShirim Rabba, “Rabbi Yehudah bar Illai said, ’He sings of me, and I sing of Him’… The congregation of Israel say to God, “Lord of the Universe, all the ills that You bring upon me are only in order to make me love You more.”
On Friday night, being the climax of the week, all the loves in a Jew’s heart come together.