A weight estimating system for estimating the weight of a mailpiece and a postage metering system including such a weight estimating system. The weight estimating system includes a measuring system, a diverter mechanism and a microprocessor system. The measuring system includes a transport, a first plurality of detectors for measuring the dimensions of the mailpiece and a second plurality of detectors for measuring values of other characteristics of the mailpiece which are indicative of the presence of non-paper materials in the mailpiece as the mailpiece is transported. The microprocessor is responsive to the second detectors to determine if non-paper materials are included in the mailpiece and, if not, determines the volume from the dimensional measurements and estimates the weight as the product of the volume and a density for paper output an appropriate postage amount to the meter and the mailpiece to the printer. The postage metering system prints the mailpiece with a postal indicium and accounts for the postage amount expended. Otherwise the microprocessor controls the diverter mechanism to reject the mailpiece for separate processing.