Why should “meter rates” go up when the meters are already paid for?

"Meter rates" are more properly called "Basic Service Charge." They are not just associated with meters, but are designed to fund the fixed expenses of operating a water system. The Basic Service Charge covers the cost of billing, maintaining and operating water system facilities, other facilities related costs, operating water quality monitoring and treatment if necessary, as well as improvements. The Commodity Charge is based on variable costs such as electric power and treatment chemicals.