Sorting is a fundamental function in many applications from data processing to database systems. For high performance, sorting-hardware based sorting designs are implemented by conventional binary or emerging stochastic computing (SC) approaches. Binary designs are fast and energy-efficient but costly to implement. SC-based designs, on the other hand, are area and power-efficient but slow and energy-hungry. So, the previous studies of the hardware-based sorting further faced scalability issues. In this work, we propose a novel scalable low-cost design for implementing sorting networks. We borrow the concept of SC for the area- and power efficiency but use weighted stochastic bit-streams to address the high latency and energy consumption issue of SC designs. A new lock and swap (LAS) unit is proposed to sort weighted bit-streams. The LAS-based sorting network can determine the result of comparing different input values early and then map the inputs to the corresponding outputs based on shorter weighted bit-streams. Experimental results show that the proposed design approach achieves much better hardware scalability than prior work. Especially, as increasing the number of inputs, the proposed scheme can reduce the energy consumption by about 3.8% - 93% compared to prior binary and SC-based designs.