In this paper, a weighted proportional fair (PF) scheduling method is proposed in the context of non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC) at the receiver side. The new scheme introduces weights that adapt the classical PF metric to the NOMA scenario, improving performance indicators and enabling new services. The distinguishing value of the proposal resides in its ability to improve long term fairness and total system throughput while achieving a high level of fairness in every scheduling slot. Finally, it is shown that the additional complexity caused by the weight calculation has only a limited impact on the overall scheduler complexity while simulation results confirm the claimed improvements making the proposal an appealing alternative for resource allocation in a cellular downlink system.