We consider a cooperative non-orthogonal multiple access system with radio frequency energy harvesting, in which a user with good channel harvests energy from its received signal and serves as a decode-and-forward relay for enhancing the performance of a user with poor channel. We here aim at maximizing the weighted sum rate of the system by optimizing the power allocation coefficient used at the source and the power splitting coefficient used at the user with good channel. By exploiting the specific structure of the considered problem, we propose a low-complexity one-dimensional search algorithm which can provide optimal solution to the problem. As a benchmark comparison, we derive analytic expressions and simple high signal-to-noise ratio (SNR) approximations of the ergodic rates achieved at two users and their weighted sum with fixed values of the power allocation and the power splitting coefficients, from which the scaling of the weighted sum in the high SNR region is revealed. Finally, we provided numerical results to demonstrate the validity of the optimized scheme. Index Terms-Cooperative NOMA, RF-energy harvesting, weighted sum rate analysis and optimization.