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 less than or equal to nu less than or equal to 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.