Social network-based Sybil defenses exploit the trust exhibited in social graphs to detect Sybil nodes that disrupt an algorithmic property (i.e., the fast mixing) in these graphs. The performance of these defenses depends on the quality of the algorithmic property and assuming a strong trust model in the underlying graph. While it is natural to think of trust value associated with the social graphs, Sybil defenses have used the social graphs without this consideration. In this paper we study paramagnetic designs to tune the performance of Sybil defenses by accounting for trust in social graphs and modeling the trust as modified random walks. Our designs are motivated by the observed relationship between the algorithmic property required for the defenses to perform well and a hypothesized trust value in the underlying graphs.