A red LED at reasonable current levels has a voltage drop of about 1.8V or 1.9V.

So with a 3V supply and 100Ω series resistor we would expect a current of about (3-1.8)/100 = 12mA

With 200Ω series resistor we would expect 6mA. Which is what you measured.

Referring to 'resistance' of a nonlinear device like an LED does not make much sense because you can't really use it to predict the current under different conditions.

A better model is a fixed voltage source. And an even better model is Shockley diode with series resistance.

There is a characteristic called dynamic resistance that does make sense in some contexts where you look at the change in voltage across the LED for the change in current. For example, you changed the current by about 5mA (from 6 to 11mA) and the LED voltage will have changed a bit. You can measure this. The dynamic resistance will be \$\Delta V\$/\$\Delta I\$. However it is useless for calculating the LED current.

Below I've simulated the two situations simultaneously (source + resistor + LED) with lots of meters to show the currents/voltages. Hopefully the clutter does not obscure how simple the situation is.

^{simulate this circuit – Schematic created using CircuitLab}

Here you can see that the voltage across the LED (using the Circuitlab model for a red LED) changes from 1.788V to 1.9V when the current is increased by 4.94 mA, so the dynamic resistance is about 22Ω. You will find that dynamic resistance is not only useless for calculating the total LED voltage or current, but varies a lot with the current, in fact it's more-or-less inversely proportional to the current.

In any case, you can see that the fixed-voltage-source model gives numbers that are in the ballpark, but the simulation model gives numbers that are even closer to what you actually measure.

A red LED at reasonable current levels has a voltage drop of about 1.8V or 1.9V.

So with a 3V supply and 100Ω series resistor we would expect a current of about (3-1.8)/100 = 12mA

With 200Ω series resistor we would expect 6mA. Which is what you measured.

Referring to 'resistance' of a nonlinear device like an LED does not make much sense because you can't really use it to predict the current under different conditions.

A better model is a fixed voltage source. And an even better model is Shockley diode with series resistance.

There is a characteristic called dynamic resistance that does make sense in some contexts where you look at the change in voltage across the LED for the change in current. For example, you changed the current by about 5mA (from 6 to 11mA) and the LED voltage will have changed a bit. You can measure this. The dynamic resistance will be \$\Delta V\$/\$\Delta I\$. However it is useless for calculating the LED current.

Below I've simulated the two situations simultaneously (source + resistor + LED) with lots of meters to show the currents/voltages. Hopefully the clutter does not obscure how simple the situation is.

^{simulate this circuit – Schematic created using CircuitLab}

Here you can see that the voltage across the LED (using the Circuitlab model for a red LED) changes from 1.788V to 1.9V when the current is increased by 4.94 mA, so the dynamic resistance is about 22Ω. You will find that dynamic resistance is not only useless for calculating the total LED voltage or current, but varies a lot with the current, in fact it's more-or-less inversely proportional to the current.

In any case, you can see that the fixed-voltage-source model gives numbers that are in the ballpark, but the simulation model gives numbers that are even closer to what you actually measure.

In most cases we use the Vf numbers from the datasheet, since that is what is provided. Usually we get limits on Vf at one or two currents and a 'typical' (which means maybe not real, certainly not guaranteed) variation of Vf with current, and that is all we have to work with for design purposes. If it is inadequate to reasonably accurately predict the current that's a hint that the LED Vf near the desired current is too high for the supply voltage and we need to increase the supply voltage or use a different LED.