Does it matter if your mix is asymmetrical?
When you listen to a stereo CD, you expect the sound from both speakers to be equally loud, most of the time. If you listened to an entire track that was skewed either to the left or right, you would think there was something wrong.
So in mixing, one of the priorities is to balance the levels between the left and the right channel. In conventional practice, the vocal, bass and kick drum are always panned exactly center, and everything else is balanced around that.
Getting a subjectively balanced mix isn't too difficult. But the situation sometimes arises where it sounds balanced subjectively, but the meters show a distinct imbalance in levels between left and right. Can you trust your ears, or should you go by the meters?
Firstly, always trust your ears, but use the meters as a guide. In this case they are guiding you into an investigation of what is happening. You can't leave your mix like this otherwise you are losing level. Where one channel is reaching its maximum peak, the other channel has several decibels going begging. Other people's mixes will sound louder than yours.
The cause of the problem is likely to be that some sounds have peaks of very short durations. They don't sound loud because they contain little energy, they come and go so quickly. Other sounds that are not so 'peaky' fill up the available dynamic range and sound louder, even though their peaks are no higher.
So the answer here is to 'chop off' the peaks by using a limiter, or a compressor set to a high ratio. That won't change the subjective quality of a peaky sound too much, but it will even out the level much better.
Now, when you re-balance your mix, you should find that both channels are around the same level, and you can optimize the peak levels of both.
By the way, those old-fashioned mechanical VU meters never were much good at reading peaks accurately, but they did give a good indication of the subjective loudness of a mix.