The influence of solar variability on climate is currently uncertain. Recent observations have indicated a possible mechanism via the influence of solar modulated cosmic rays on global cloud cover. Here we show that the influence of solar variability is strongest in low clouds (<= 3.2km). These are liquid water clouds which points to a microphysical mechanism involving enhanced aerosol formation. If confirmed it suggests that the average state of the Heliosphere is important for climate on Earth. The estimated response in low clouds due to a doubling of solar activity is a 1.4 W/m2 warming.