The electron spin resonance (ESR) of conduction electrons is reported for the weak itinerant ferromagnet ScIn which, upon chemical substitution with Lu, shows a suppression of ferromagnetic correlations. A well-defined ESR lineshape of Dysonian type characterizes the spectra. The ESR linewidth, determined by the spin dynamics, displays a broad minimum only for the ScIn compound. We discuss the results using the mechanism of exchange enhancement of spin-lifetimes.