TOOFIF:If you phone in a reading every month you could save hundreds of pounds during mild periods and be capped at a monthly seasonal maximum during cold spells.
I doubt you can save hundreds of pounds but you're dead right right to be alert to the system (and to be annoyed that the system is difficult to spreadsheet).
For most people who have annual consumption in excess of 4572 units the main effect will be to load primary unit cost onto the winter bill and anybody who switches just after the winter period will lose out. Maybe that is the idea. The total cost after a year will not be affected by weighting and to be fair NP have a leaflet which describes the system as clearly as it's possible to describe such a complicated system.
If you switch to NP SignOnline the weighted system is not used. Another sneaky NP "idea" on their cheapest unweighted tariffs, which to be fair are the "cheapest" available by quite a way, is only to pay the discount after 12 months. Again anybody who switches before the discount is received loses out.
EON also have a sneaky variation on this.
The lesson is to be alert to these "scams" which unfortunately the regulator OFGEM seems to be currently allowing.