In this paper, the performance of dual-hop decode-and-forward (DF) cognitive relay networks over independent non-identically distributed (i.n.i.d.) Weibull fading channels are evaluated, in a spectrum sharing environment. Where the transmit power of the secondary network is governed by the maximum interference power that the primary networks' receiver can tolerate. The closed form outage probability (OP), symbol error probability (SEP) and the ergodic capacity under interference power constraints from the primary network over i.n.i.d. Weibull fading channels are derived using statistical characteristics of the signal-to-noise ratio (SNR). The analytical results are verified by Monte-Carlo simulation.