Capacitor not reaching supply voltage with LED in series
A LED is a device with very non-linear internal impedance as a function of applied voltage. When the forward voltage is under 1-1.5 V, LEDs have very high impedance, few u-Amps at 1 V, which amounts to 300- 500 kOhm of effective impedance.

 

The LED current in this area is so low that it is not even characterized in many datasheets.

On the other hand, electrolytic capacitors have substantial leakage, as shown in this model picture:



Per this article, the leakage can be in 5 to 20 uA per 1 uF of capacitance. Therefore, a 100 uF capacitor is expected to conduct maybe 500 uA of DC current. 

So what you see is a voltage divider between the low-voltage impedance of LED and the parasitic leakage impedance of electrolytic capacitor. At 500 uA your LED has forward voltage of about 1.6V, this is what your experiment reveals.

ADDITION: Here is the typical I-V curve for a LED in area of interest, at low forward voltages, all on SE EE site.