We study online job scheduling on a processor that can vary its speed dynamically to manage its power. We attempt to extend the recent success in analyzing total unweighted flow time plus energy to total weighted flow time plus energy. We first consider the non-clairvoyant setting where the size of a job is only known when the job finishes. We show an online algorithm WLAPS that is 82 -competitive for weighted flow time plus energy under the traditional power model, which assumes the power P(s) to run the processor at speed s to be s