The electronic conductivity has been measured in homogeneous, weakly insulating, amorphous nickel-silicon films located just below the metal-insulator transition (MIT). The conductivity follows a simple CTz power-law dependence with z ≈ 1/2 over a large temperature interval. In contrast, a Mott variable-range hopping expression could not be fitted successfully through these zero-field conductivity data. The CTz behaviour can be explained using the three-dimensional (3D) electron-electron interaction (EEI) theory. The negative magnetoconductance data observed in these weakly insulating films can be fitted nicely using only the 3D EEI theory. A crossover of the conductivity from the simply power-law CTz dependence at high temperatures to an activated hopping-law dependence in the liquid helium temperature region is observed; this transition is attributed to changes in the energy dependence of the density of states near the Fermi level. The conductivity of these weakly insulating films can be fitted well over three decades of temperature using an empirical scaling expression suggested by Möbius et al.