Dusty starless cores play an important role in regulating the initial phases of the formation of stars and planets. In their interiors, dust grains coagulate and ice mantles form, thereby changing the millimeter emissivities and hence the ability to cool. We mapped four regions with more than a dozen cores in the nearby Galactic filaments of Taurus and Perseus using the NIKA2 camera at the IRAM 30-meter telescope. Combining the 1mm to 2mm flux ratio maps with dust temperature maps from Herschel allowed to create maps of the dust emissivity index   at resolutions of 2430 and 5600 a.u. in Taurus and Perseus, respectively. Here, we study the variation with total column densities and environment.   values at the core centers ( mag) vary significantly between and . Several cores show a strong rise of   from the outskirts at mag to the peaks of optical extinctions, consistent with the predictions of grain models and the gradual build-up of ice mantles on coagulated grains in the dense interiors of starless cores.