400 Hz requires much less iron in the magnetic flux path of transformers and motors, compared to 50/60 Hz.
800 Hz was even lighter, and was used for a while in several military aircraft of the 50s & 60s. Never really caught on though.
But solid state inverters / DC-DC converters use much higher frequencies (several KHz) to achieve much lighter weight. The power supply in your computer is such a device.