This paper considers discrete-time networked control systems in which distributed sensors, controllers, and actuators communicate through a shared communication medium that introduces large and bounded time-varying transmission delays. Access to the communication medium is orchestrated by a weighted try-once-discard protocol that determines which sensor node can access the network and transmit its corresponding data. The closed-loop system is modelled as a novel discrete-time hybrid system with time-varying delays in the dynamics and in the reset conditions. By Lyapunov method a new condition is derived for the exponential stability of the delayed hybrid systems with respect to the full state and not only to the partial state. An example of a discrete-time cart-pendulum illustrates the efficiency of the time-delay approach.