In this paper, we present a pull-based dissemination protocol for efficient distribution of scalable video content in overlay peer-to-peer networks with mesh structures. The proposed protocol employs prioritized network coding, where the network coded packets belong to classes that represent packets of different priorities. For a receiver, the pull procedure begins with the reception of buffer vector messages from the senders, which bring information about the numbers and classes of available packets. The receiver node decides on the rate allocation of the different classes to be requested from each of the senders. The rate allocation is cast as a video quality maximization problem and solved using a hill-climbing algorithm. The simulation results show that the proposed mechanism, which is able to fully adapt to network dynamics, accounts for the unequal packet importances and utilizes the network resources efficiently.