Middle East, Mediterranean, and western Europe:
The seven stellar objects visible to the naked eye, moving in the heavens like living objects, were attributed to gods by the ancients. The planet gods are similar between Sumerians and the Romans.... Names of weekdays are derived from these seven planets.
The order is not explained, as inner or outer, therein.
Wikipedia also tells elsewhere, 'Sanskrit attestations of the navagraha "nine astrological forces", seven of which are used for day names, date to the Yavanajataka "Sayings of the Greeks", a 150 CE translation of a 120 CE Greek Alexandrian text'.
i.e this seven names have come to be associated with Hindu calender since 150 CE, i.e. in other words, during the Mahabharat days, the system or at least the names might have been different. Perhaps, they were referred as the nth day after Full Moon day/No Moon day: (Prathamya, etc and fortnights, paksh and no week as such).
All the same, it is intersting to note that the systems prevalent in many regions of the world have evolved in diferent routes, but zeroed on one comparable and willy-nilly uniform names.