We report a significant increase in the reflectivity of a soft x-ray Co/C multilayer at grazing incidence after low-temperature annealing. By monitoring the enhancement of the first-order modulation peak on annealing, an effective interdiffusion coefficient as low as has been measured, which is nearly equal to the true macroscopic interdiffusion coefficient as the modulation wavelength of the Co/C multilayer studied is well above the critical wavelength. The negative true macroscopic interdiffusion coefficient indicates that there is a tendency to phase separation in the Co - C system, which can be interpreted as the positive enthalpy of mixing calculated on the basis of Miedema's macroscopic atom model. The decrease in reflectivity above some annealing temperature is also discussed and explained as the competition between interfacial sharpness and roughness. This is the first report of observations of enhanced reflectivity in the Co/C multilayered system.