Rotary switch to turn LEDs on cumulatively
This answer was written before the OP commented that s/he is using a 3.2 V supply.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The simplest option if a high enough voltage supply is available. With SW8 closed D1 to D7 will light.







simulate this circuit

Figure 2. For lower supply voltages the chain can be split. In this case SW8 being closed lights D7 but also provides a ground to light all the LEDs in the upper chain.

You can further refine Figure 2 for lower supply voltages but would require more and more diodes.



Figure 3. A single-pole 12-way switch will suffice.



Constant current sources (by me):


AL5809 constant current driver.
Simple constant current driver. (This is in the negative line.)