Neutrons created in fusion reactions carry information about the ions taking part in the reactions. By measuring the energy spectra of neutrons from a fusion plasma, it is thus possible to gain information on the velocity-distribution of the ions. Here, we describe the velocity-space sensitivity of energy spectra of neutrons produced in the fusion process between a thermal ion and a fast ion. The velocity-space sensitivities of fast-ion diagnostics are described by socalled weight functions. Weight functions have previously been calculated for neutron yield detectors, neutral particle analyzers, fast-ion Df spectroscopy (FIDA) and collective Thomson scattering (CTS). Here we present weight functions for neutron emission spectrometry (NES) and show examples of their applications using data from the time-of-flight neutron spectrometer TOFOR at JET.