In Wireless Networked Control Systems (WNCSs), the feedback control loops are closed over a wireless communication network. The proliferation of WNCSs requires efficient network resource management mechanisms since the control performance is significantly affected by the impairments caused by network limitations. In conventional communication networks, the amount of transmitted data is one of the key performance indicators. In contrast, in WNCSs, the efficiency of the network is measured by its ability to facilitate control applications, and the data transmission rate should be limited to avoid network congestion. In this work, we consider an experimental setup where multiple control loops share a wireless communication network. Our testbed comprises up to five control loops that include Zolertia Re-Mote devices implementing IEEE 802.15.4 standard. We propose a novel relevance- and network-aware transport layer (TL) scheme for WNCSs. The proposed scheme admits the most important measurements for the control process into the network while considering current network conditions. Moreover, we propose a mechanism for the scheme parameters adaptation in dynamic scenarios with unknown network statistics. Unlike the conventional TL mechanisms failing to provide adequate control performance due to either congestion in the network or inefficient utilization of available resources, our method prevents network congestion while keeping the control performance high. We argue that relevance- and network-awareness are critical components of network protocol design to avoid control performance degradation in practice.