Remarkable nonlinearities in the differential tunneling conductance between fractional quantum Hall edge states at a constriction are observed in the weak-backscattering regime. In the nu=1/3 state a peak develops as temperature is increased and its width is determined by the fractional charge. In the range 2/3</=nu</=1/3 this width displays a symmetric behavior around nu=1/2. We discuss the consistency of these results with available theoretical predictions for interedge quasiparticle tunneling in the weak-backscattering regime.