1. A check transaction processing system using a customer's checking account identification number as a unique customer identification code (“check ID”) comprising: a transaction processor for processing check transactions for a store, and for storing a customer database, including customer records, for that store; each customer record being uniquely identified by the customer's check ID, and including selected customer information; said customer information including check verification status information such that a customer is assigned one of the following check verification status values: POSITIVE—the customer's check transaction history meets preselected positive criteria for authorizing the check transaction; NEGATIVE—the customer's check transaction history meets preselected negative criteria for not authorizing the check transaction; or CAUTION—the customer's check transaction history meets neither the positive or negative criteria, so that authorization of the check transaction depends upon predetermined interim criteria. said customer information including check transaction data about the customer's check transaction history (including frequency and dollar volume over selected intervals), which is updated for each check transaction to reflect the current check transaction. at least one transaction terminal located at a point-of-sale and remotely coupled to said transaction processor for transmitting customer information requests to, and receiving customer information responses from, said transaction processor; each customer information request including the customer's check ID and a function code identifying the information requested; one of the customer-information-request function codes designating a check transaction verification function in which the corresponding customer information response is used for check transaction authorization. said transaction processor processing each customer information request by: retreiving the corresponding customer record, if it exists in the customer database; and generating a customer information response in accordance with the function code in the customer information request, reflecting either the customer information in the customer record, or the absence of such a customer record in the customer database.