Actually, the days were not dedicated to any particular god, but to particular planets as per jyotishi. Since the astrologers calculated and formulated rules for time keeping, they used celestial objects as their reference. So each day is dedicated to a particular celestial object found in astrology:
Ravi-var (Ravi - Sun)
Soma-var (Soma - Moon)
Mangal-var (Mangal - Mars)
Budha-var (Budha - Mercury)
Guru-var / Brihaspati-var (Guru/Brihaspati - Jupiter)
Shukra-var (Shukra - Venus)
Shani-var (Shani - Saturn)
But later on due to different reasons like a god's appearance, birth day, or as certain events in mythology took place on a specific day, that day was started to be celebrated for that particular god.
For example, it is believed that Hanuman was born on a Tuesday. Hence, that day is dedicated to him. Lord Shiva holds up the moon on his head, hence known as Chandrasekhara. So moonday (Monday) is dedicated to Shiva. Thursday being dedicated to Brihaspati, the guru of gods, Lord Vishnu is worshipped on this day. It is because Lord Vishnu is Brihaspati Himself:
purodhasāṁ ca mukhyaṁ māṁ viddhi pārtha bṛhaspatim [BG - 10.24]
O Partha (Arjuna), know Me as Brihaspati, the chief of all priests.
Similarly, from other folk stories like Santhosi Mata Vrat, certain days like Friday gained prominence for a particular deity or god. But at the end of the day, all days are actually dedicated to a particular planet as per our jyotishi system.