what happens electronically when you increase resistance
In a series circuit, the voltage across a resistor is directly proportional with its resistance (Et= I(Rint+R). That means in a series circuit the voltage across the resistor will increase when the resistance in increased, while the current will reduce. A power source has internal resistance (Rint) which will be in series with the resistor R. So even though your resistor is connected across the power supply, the internal resistance Rint is in series with it.