I'm not sure if this is the fault of the recordings and room acoustics, or my Babyface Pro has something to do with it.

Firstly, I can see in Total Mix that in many recordings, that most of the time the right channel simply has higher output level.

It is not just in few recordings, but in the vast majority of recordings that I listen to.

Secondly, left channel always sounds weaker, with few different pair of speakers.

Having that said, room acoustic might has something to do with it, and there are few recordings that the output level on both channel seems more balanced when looking on Total Mix.

Here is a good example where Total Mix shows me much much higher output level on the right channel:
https://www.youtube.com/watch?v=3K7pgufblmQ

You can check for yourselves and tell me what you see, this will help me to understand my situation and I'll be very thankful.