A potential solution to the weight transport problem, which questions the biological plausibility of the backpropagation of error algorithm, is proposed. We derive our method based upon an (approximate) analysis of the dynamics of leaky integrate-and-fire neurons. We thereafter validate our method and show that the use of spike timing alone out-competes existing biologically plausible methods for synaptic weight inference in spiking neural network models. Furthermore, our proposed method is also more flexible, being applicable to any spiking neuron model, is conservative in how many parameters are required for implementation and can be deployed in an online-fashion with minimal computational overhead. These features, together with its biological plausibility, make it an attractive candidate technique for weight inference at single synapses.