Employing reconfigurable intelligent surfaces (RIS) is emerging as a game-changer candidate, thanks to their unique capabilities in improving the power efficiency and supporting the ubiquity of future wireless communication systems. Conventionally, a wireless network design has been limited to the communicating end points, i.e., the transmitter and the receiver. In general, we take advantage of the imposed channel state knowledge to manipulate the transmitted signal and to improve the detection quality at the receiver. With the aid of RISs, and to some extent, the propagation channel has become a part of the design problem. In this paper, we consider a single-input single-output cooperative network and investigate the effect of using RISs in enhancing the physical layer security of the system. Specifically, we formulate an optimization problem to study the effectiveness of the RIS in improving the system secrecy by introducing a weighted variant of the secrecy capacity definition. Numerical simulations are provided to show the design trade-offs and to present the superiority of RIS-assisted networks over the conventional ones in terms of the system's secrecy performance.