‘Abdu’l-Bahá gives no reason whatever why Friday has been chosen as the day of rest in the Bahá’í calendar. He just affirms it.
(Shoghi Effendi, Lights of Guidance, p. 109)
God has created Friday for purity and pleasantness, and the resting of His servants from what they undertake on other days (The Bab, Persian Bayan, Vahid 7, 17)
Regarding the recitation on Fridays of the following verse while facing the sun “Glory (Bahá) from God be upon your rising, O sign of the countenance [of God]. Bear witness to that to which God himself has borne witness: that there is no God but him, the adored, the Best Beloved."
This is because God the Knowing has created Friday for the purity, refinement and rest of the servants from that with which they are burdened during the [other] six days, and every act performed on the day or night of Friday is rewarded like [an act performed for] a whole week, and also because the spirit of every thing depends on man, and the witness borne by every thing is the witness borne by man. Therefore it is ordained that on Friday, in the presence of the sun, people should take it as a witness to that which is more powerful, to their confession of unity of God, to their faith in the point of the Bayan, and in that which is revealed in it. May the same be said on the day of resurrection in the presence of the sun of reality, and may witness be given to the unity of God in his presence and to the veracity of whoever obeys him. This is the fruit of this command, for those of understanding.
There is no doubt that following the manifestation of the Cause, every soul, on Friday, will recite, but on the day of resurrection this will be effaced unless you recite in the presence of God. On the day of revelation it is obligatory for all to recite these words every Friday in the presence of him whom God will make manifest. [This applies to] whoever may be in his presence, providing he has given ear to whatever may please Him in that revelation, “He does what he wills, and whatever he wishes: he is not to be questioned about his acts, but all are questioned about all things.
(The Bab, The Persian Bayan, p. 342 of the INBA version)
Q. Which day of the week will the Baháis eventually observe as a day of rest?
(‘Abdu’l-Bahá, Star of the West, Vol 1, No. 12, p. 2)