Traffic load is a factor that causes damage on a bridge. It is known that many overloaded trucks are running. Information on actual traffic loads is therefore valuable, which would help construct maintenance scheme of bridges. The development of the method that weighs a truck in motion has thus attracted many highway engineers. A class of such methods makes use of bridge-girder deformation. The method is known as bridge-weigh-in-motion (BWIM). Although less expensive than a truck scale, the conventional BWIM requires the measurement of many strains in main girders and in transverse stiffeners. BWIM based on the strains in transverse stiffeners only has been tried out then. It was successful for truck-load estimation and extended to axle-load estimation. Nonetheless, when another truck is in the adjacent lane, the method became involved to keep a certain accuracy. In the present study, transverse stiffeners the strains of which are not influenced much by a truck in the adjacent lane are identified as a first step. Using such transverse stiffeners, the axle-load estimation is carried out and the achievement of the acceptable accuracy is confirmed without making the method involved. The proposed approach is then applied to a bridge on an urban expressway. Many overloaded trucks are found to travel even though the bridge is located in a local city.