Are earthquakes connected to erosion

Earthquakes are not normally related to the weather in any way. Earthquakes are studied in the science of seismology which is a sub branch of geophysics. The science of weather on the other hand is known as meteorology.

However at the same time seismic activity can be induced by increases in pore water pressure however rainfall is not usually enough on it's own to drive up pore water pressure to such an extent that this would occur.