Transformer Noise
The core of a transformer changes size with the magnetic flux inside it. The normal noise is 120Hz, 240Hz, 360Hz, etc. The sound level is proportional to the voltage. As the voltage increases, the flux in the core increases, the core vibration increases, and the sound output increases.
Change the primary tap on the transformer to a higher voltage to reduce the flux in the core and the sound will reduce.
Parasitic vibrations occur when the enclosure, mounting parts, etc. vibrate with the core. These need tightening or sound damping material applied.
The sound level DOES NOT vary with transformer loading, except to the extent that supply voltage varies with loading.