Most Hindu festivals are pinned to a Lunar day or Tithi like Rama-navami, hera-pancami etc. The 7-day week runs out-of-sync with the lunar tithis; it would be very confusing to try to follow both at the same time.
Yet many astrological sites also assign deities and planets to the 7-day week days. Is it just a recent western superimposition? Or are there any references to vasara or weekdays in the scriptures?
The Hindu equivalent for the modern weekday is called as vāsara or vāra in the modern usage. Ravi-Vāsara, Som-Vāsara, Mangal-Vāsara etc, which are equivalent of Sunday, Monday and Tuesday do bear a striking resemblance etymologically.
Although Vāsaras do not serve any computational purpose, unlike Tithis, which are used to determine a day in the lunar calendar, they still do form one of the five angas of the Hindu Panchanga, the other four being tithi, nakshatra, yoga and karna. They are also mentioned in the Vedanga Jyotisha which is considered to be the origin of Hindu Astrology.
As for what could be the origin of this system, the answer is the Navagrahas: Surya(Ravi, Sun),Som(Moon),Mangal(Mars), Budha(Mercura), Guru(Jupiter), Shukra(Venus), Shani(Saturn), Rahu and Ketu.
The first seven preside over individual Vāsaras while Rahu and Ketu are responsible for the Solar and Lunar eclipses. All these nine Grahas are said to move with respect to the fixed constellations in the zodiac, hence influencing the lives of the people affected by the respective constellations. It is not very unlike the western belief in astrology where different deities were said to preside over the opening hours of the days named after them.
So it is not just a westernised version of our own system. Tithis and Vāsaras exist independently of each other and fulfill different requirements. Tithis have more significance in the field of Astronomy for maintaining calendars and predicting celestial events like eclipses, Vāsaras have Astrological significance, helping determine the effect of the current arrangement of stars on the life of an individual.
But as with everything else in Hinduism, Astronomy and Astrology are closely related and these two are easily mixed up with one another. It is better to keep track of tithis for the purposes of a calendar of events.
The Shiva Purana Vidyeshwara Samhita mentions Lord Shiva creating the seven days of a week and assigning deities to them. It states that in the very first creation the seven days were ordained by the Lord for different reasons:
At the beginning of the first creation, the omniscient, merciful lord Mahādeva created the different week days for the benefit of the entire world.
Lord Mahādeva, the global physician, the omniscient, the panacea of all panaceas, made the first day his own day that bestows good health.
Next he created the day of his Māyā (Illusion) the bestower of prosperity.
Afterwards when the birth of Kumāra was attended with some mishaps he created the day for the sake of surmounting mishaps and idleness.
With a desire to bless the worlds and for their nurture and protection he created the next day dedicated to Viṣṇu, the protector of the worlds.
The next day created by the lord is for the sake of the longevity of the worlds dedicated to the creator of the three worlds, Brahmā, called also Parameṣṭhin, who is the bestower of longevity too. Hence this day too bestows longevity.
The last two days of the week created by the lord are those of Indra and Yama. In the beginning when the lord created Puṇya and Pāpa (Virtue and Sin) for making the three worlds flourish, these deities who preside over them were assigned these two days. The last two days are the bestowers of worldly enjoyments and removers of premature death respectively. The lord made the sun etc. who are His own manifestations and are firmly established in the solar cycle the lords of the different days.
So as per the Shiva Puran, the weekdays have been in existence since the first creation and are also associated with celestial bodies like the Sun and the Navagriha.
The Devi Bhagvat Puran also mentions this regarding time:
(O Nārada! Now I will speak of time.) The seven days of the week, Sunday, &c., the sixteen tithis, Pratipada &c., the twelve months Vaiśākha &c., the six seasons Summer, &c., the two fortnights (dark and bright) and the two Ayaṇas (Northern and Southern) are rendered in vogue. One day consists of four Praharas, one night consists of four Praharas; a day and a night constitute one so-called day. Thirty such days make one month.
There may be more such examples in the Purana and I'll add those as well if I come across them.
