The effect of grounding a simple circuit?
The Earth's huge capacitance means that it can exchange a lot of charge without changing potential. Your circuit, however, has a comparatively tiny capacitance. If some charge is added or taken, it changes potential a lot (compared to the change in the potential of the Earth). So it is not the Earth changing its potential to meet the circuit, it is the reverse -- the circuit changes its potential to match that of the Earth.
More formally, we should really consider the capacitance of the Earth-circuit system and ask how much the voltage between the two changes if some charge is moved from one to the other. However, the change in the electric field between them, which determines the change in voltage, is all due to the change in the electric field due to the charge transfer to or from the circuit rather than from the Earth.