Why does per-led current consumption diminishes when more leds are on?
If using a constant voltage source it is advisable to use current limiting resistors in series with LEDs.

If these LEDs are different colors that may explain the different current readings.

Or, if all LEDs are of the same color and you are powering the project from a source with internal resistance (a battery), the more current you draw the lower the supply voltage.  This may show up as a reduced incremental current increase.

Or, if using a poor power source or operating at the current capacity of the power supply - again - this may show up as a reduced incremental current increase.

Note that different generations of LEDs operate at slightly different voltages.  But, in general, RED, GREEN &amp; BLUE LEDs of the same generation operate at slightly increasing voltages respectively.  Details can be found here in this wikipedia.com page:


  Typically, the forward voltage of an LED is between 1.8 and 3.3 volts.
  It varies by the color of the LED. A red LED typically drops 1.8
  volts, but since both voltage drop and light frequency increase with
  band gap, a blue LED may drop from 3 to 3.3 volts.


Use the LED current (Iled) and voltage (Vled) specifications to determine the proper resistor value for a given supply voltage (Vbatt).

The following equation from this article should prove useful for this calculation: