We investigate the variability of solar Balmer lines (H-alpha, beta, gamma, delta) observed by space-borne radiometers (SORCE, SCIAMACHY, GOME-2, OMI, and TROPOMI), combining these precise, long-term observations with abundant, high-resolution data from the ground-based NSO/ISS spectrograph. We relate the detected variability to the appearance of magnetic features on the solar disk. We find that on solar-rotation timescales Balmer line activity indices (defined as line-core to line-wing ratios) closely follow variations in the total solar irradiance (which is predominantly photospheric), thus frequently (specifically, during passages of big sunspot groups) deviates from behavior of the line-activity indices that track chromospheric activity levels. At longer timescales (years), the correlation with chromospheric indices increases, with periods of low- or even anti- correlation found at intermediate timescales. Comparisons with Balmer-line variability patterns obtained from a semi-empirical model indicate that it is unlikely that the periods of low/anti correlations can be ascribed to the presence of filaments, in contradiction to some previous studies.