I find it easier not to drop too deeply into the physics....
Like someone else said, electrons flowing around a circuit are not unlike water molecules flowing through a pipe.
Voltage is a lot like pressure. Imagine a bucket of water with a hose coming out of it that hangs 1 meter high. There is a pressure, that is just determined by the height. If we measure it really near the ground - even if the hose is clamped off - it is simply a number (that is just the density times the height).
Now, if the hose is a 1 inch diameter hose, and we release the clamp, water will flow to ground from the bucket through it at some rate. The hose has some 'resistance' (friction), and for a give pressure a fixed rate of water (a current, measured in molecules per second) will drain per second.
Now imagine pinching the hose. The pressure is the same, but there is more resistance: thus, there is less flow per second.
Electricity is pretty similar. Electrically, pressure is 'voltage' and flow is 'current' - just like the current in a river (which is where the term comes from). Current is the number of electrons per second, if you will, that go through the hose (or 'circuit'). SO, for a given pressure, with less resistance there is more current.
All of the electrons that flow must flow through the resistor, just like all the water that flows must flow through the hose - whether wide-open or pinched. But when we talk about current we care about the flow rate. There isn't a set of molecules (or electrons) on one side and a set on the other. Yes, at any instant there is, just like at any instant some of the water molecules are in the bucket, some above the pinch in the hose, and some on the ground that have already flowed. But we are interested in flow rates (electrons per second), not a snapshot.
It is actually easier, I find, to think of it like circuit designers do: there is a supply voltage, and a ground where all the electricity wants to go, just as all water wants to flow downhill, and stuff in-between. (Warning: usually, we call that voltage positive, so to be accurate electrons are flowing backwards - but that is just a convention.)
Now ask yourself the same questions you had asked. The voltage (pressure) is what it is. The resistance is what it is (call it R). By definition, the amount of electrons that can flow through the resistor to ground per second (the current, I) for a fixed pressure (the voltage, E) is related by a very simply formula:
E = IR
So, if E = 9V, R = 1 ohm, then the current I = 9 amps. But if E = 9V and R = 9 ohms, the current (I) is reduced to 1 amp.
Where you are getting confused is imagining electrons are getting stuck in the resistor, or leaking out of it. But, if we pinch off a hose no water gets stuck or leaks at the pinch: every molecule eventually goes through; the rate it happens at just gets slowed down by more resistance.