They just seem to be following their print model for some sort of mental connection in buyers used to paying for weekly newspaper subscriptions. It's confusing to me to figure out as someone who prefers monthly installments (UK rent is figured per week as well, then multiplied by 52, then divided by 12 for the monthly rent… so convoluted), but it's not totally bizarre for NYTimes to bill this way.
alternatively, a way to accurately measure their accounting week by week?