There is an increasing demand for Internet of Things (IoT) systems comprised of resource-constrained sensor and actuator nodes executing increasingly complex applications, possibly simultaneously. IoT devices will not be able to execute computationally expensive tasks and will require more powerful computing nodes, called edge nodes, for such execution, in a process called computation offloading. When multiple powerful nodes are available, a selection problem arises: which edge node should a task be submitted to? This problem is even more acute when the system is subjected to attacks, such as DoS, or network perturbations such as system overload. In this paper, we present a trust model-based system architecture for computation offloading, based on behavioural evidence. The system architecture provides confidentiality, authentication and non-repudiation of messages in required scenarios and will operate within the resource constraints of embedded IoT nodes. We demonstrate the viability of the architecture with an example deployment of Beta Reputation System trust model on real hardware.