Detection of weak signals remains challenging in astrophysics. This is particularly applicable in the investigation of Forbush events. There is thus, a paucity of catalogs of small-amplitude Forbush decreases (FDs). Detail investigations of the space-weather implications of small FDs are, thus, lacking in the literature. Recently, large catalogs of weak FDs, for the first time, have been published. This work employs the newly created lists of small-amplitude FDs to investigate the statistical link between small FDs and solar-geomagnetic variables. The solar-geomagnetic variables were obtained from the OMNI database. A simple coincident R software code was employed in matching the related solar-geomagnetic variables with the weak Forbush events. The FD dates were taken as the input signal. Scatter plots of FDs against interplanetary magnetic field (IMF), solar wind speed (SWS), planetary K-index (Kp) and planetary A-index (Ap) reveal a negative relationship, while that of FDs against disturbance storm time index (Dst) shows a positive relationship. Statistical significance of these relations were tested. The small-amplitude FDs and solar-geomagnetic variables at Potchefstroom (PTFM) station register statistically significant relations. Non-statistically significant correlation between the small-amplitude FDs and solar-geomagnetic variables were obtained at South Pole (SOPO) station, with the exception of FD-SWS that reveals statistically significant correlation. The differences in the correlation results obtained at the two stations (PTFM and SOPO) could be attributed to the differences in the characteristics of the NM stations. These results suggest that geomagnetic storm indices play important role in the evolution of FDs.