Why headphones doesn't work with mic out port?
Microphones output at mic level, which is a signal that ranges from around 0.001 volts to 0.01 volts. Headphones work at closer line level, which is around 1 volt. Based off that information, you can see there isn't enough power in the output of a microphone to hear it by directly plugging headphones into the microphone. Just because they have the same connector, doesn't mean that the signals are compatible. This isn't Sony design flaw, it is how all microphones work.

Instead of plugging the headphones directly into the microphone, you need to use a headphone amplifier. Connect that directly to the mic and then plug your headphones in to the amp. There are headphone amps available in a number of price ranges, depending on the features and quality you need.