Western seven-day week comes from ancient near east, one of the explanations for it is that it started as an approximation for a quarter of the lunar cycle.

As for weeks of different lengths, the ancient Egyptian calendar divided each 30 day month into three 10 day weeks. Additionally, the Welsh word for a week means "eight nights", which might refer to an eight day week, but might also be an example of inclusive counting (i.e. the last day of cycle is also the first day of next cycle).

There's always room for discussion, but perhaps the section Calendars and Timekeeping from our FAQ will answer your inquiry.