At some point, “running more” pretty much becomes “increasing weekly mileage,” because that’s how most runners track things.
Weekly mileage might not be the best framing device for tracking how much you run. You might make the common mistake of viewing each week as its own entity, with things that “have” to happen in that week for the week to be successful. Similarly, you might tend to view your training primarily in blocks of a week, rather than a broader view that more accurately reflects how your body responds to the stimulus of running. Tracking monthly mileage so that you don’t artificially force certain things to happen within each horizontal strip of a calendar might be a more prudent approach.
But most of the rest of our lives are shaped by the week’s seven-day cycle, so it makes some sense for a week to be the next unit of training after a day.