All vehicles in NZ pay road user charges; EVs have just been exempt to encourage uptake. There are RUC weight classes but they only exist to separate light (<3500kg) and heavy (>=3500kg) vehicles rather than distinguish between a Nissan Leaf (1600kg) and a Ford Ranger (2100kg).
Uh, no. All non-petrol powered vehicles pay road user charges.
For petrol vehicles we tax the petrol instead. This is because the cost of compliance is much cheaper (for the government and the car owner) if we tax the petrol. We don't do that for desil vehicles because a large about of desil is used by farm equipment and other off road vehicles. It's easier to do road user charges than to have a refund scheme for desil taxes.