Did these arise from some common source predating both (PIE?), or was the Graeco-Roman week imported into India at some later point in time?
None of the Hindu mythological books or puranas mention the names of the week , today what we use as VAAR ( Ravi , Som , Mangal, Budh . Brihaspati, Shukra, and Shani ) are the translated version of the western system , it was only the THITHI as per the Lunar calendar followed all over. the names of the week is recent and has no origin in Indian Mythology ( any religion that is followed in India ).
The ancient Hindus did not regularly use "days of the week" (although they are attested). The reason for this was that the Hindu calendar before 1100 AD used mean times (called madhyama) and this can shift days from one month to another. They did have a division into days assigned as one day to each planet as follows:
This is only one possible naming scheme, and many others can be found in ancient Indian writings.
More important among the ancient Hindus was the lunisolar calendar in which each day was numbered, similar to the method of the Romans. Like the Romans the month was divided into two 15-day fortnights, the first being suddha (waxing) and the second being bahula (waning).
Note that there is no regular calendar in India, but many of them in common use for various purposes. It is estimated that today there are about 30 different commonly used calendars in India.
"Calendrical Calculations" by Dershowitz and Reingold (Cambridge University Press, 2008).
To the extent that the Indians use the Norse names of the week is due to the influence of the Portuguese and English.
The seven day week is Sumerian or Babylonian in origin. The astrological component is also Babylonian. Seven was an important number to the Babylonians; the world was created in seven days, the Annunaki were seven gods.
The Persians and Jews adopted it from the Chaldeans. The Greeks adopted it in the 4th century B.C. It became common in Rome during the early imperial era, due to an influx of Hellenism and Judaism. It superseded the Roman 8 day week by the end of the Julio-Claudian period, but it wasn't made official until Constantine. (1)
The 7 day week appears in Indian history during the Gupta period (3rd-5th centuries A.D.). Its similar appearance in China during the fourth century is attributed to Manichaean monks. (1)
(1) Wikipedia- Week
Hinduism is not the birth place of week days or planets! Shocked ?! .. read on .. That’s because there were several INdian religions in India before everything were combined into one in the recent centuries So coming to the answer about week days you can see more than two thousand year old temples in south india that has deities for each planet Sunday first because it takes only one day for revolution around earth moon takes a month followed by other planets that could be the reason for sequence thanks