The transformer windings might be an bit loose and start to vibrate when you pull an big load off it.
One pointer should be that the voltage doesn't change when under load, meaning the output and rectification and voltage regulation is oke.
What's left is the mechanical sound from the windings/core of the transformer, i used to put the whole transformer in an bath of epoxy to cure that, only leaving the connector(s) free of it.
This doesn't mean the transformer is bad, just sloppy work making it...
If you can get into the windings with an syringe or an hot glue gun, that would work too, do DISCONNECT from the MAINS before doing any work on it..
If the core is visible, treat the metal core the same.
Then, mount the transformer on rubber feet to dampen the vibrations.
Or mount an replacement good tranformer, same voltage, same amps output, higher amps is no problem, but keep the output voltage the same.
Cor