Output impedance and loudness
I'm currently using Sony MDREX110AP headphones, with 16 ohm impedance
  according to its specs. When I connect them to the 0.47 Ohm output I
  get much louder output than with the 47 Ohm jack


Possible explanation.....


The socket labelled 47 ohm has an output impedance of 47 ohms. This means that with a 16 ohm load and, using the voltage potential divider equation, the output will be reduced from an open-circuit voltage of (say) X to a value that is about 0.254 X.

The socket labelled 0.47 ohm has virtually zero output impedance compared to a load of 16 ohms hence the output is barely attenuated.

A reduction in signal voltage level to 0.254 is an attenuation of nearly 12 dB which is more than halving the loudness level (based on 10 dB being a halving or doubling of perceived loudness at 1 kHz).