Why aren't resistors lowering the current flowing in my circuit?
I can't tell you what the problem is with your apparatus since the photos can only give a limited amount of information.

However, it appears from the photo that you just have a voltage source (battery) in series with a resistor in series with an ammeter (you do have the multimeter set up to measure current and the leads connected to the proper inputs, correct?).

Now, this is certainly a valid connection and, if the above is a correct description, you should be able to measure different current values for different resistor values (however, if your multimeter and leads are set to measure voltage instead, you will only measure the battery voltage regardless of the resistor value).

However, with such a simple circuit, you can simply use Ohm's law to calculate the current.

Since an ammeter is effectively a short circuit, the current through the resistor is simply the battery voltage divided by the resistance.

In other words, if you simply connect the resistor directly across the battery and then measure the voltage across the parallel combination, the current is simply the measured voltage divided by the measured resistance.