What is your MacBook Pro's sub-model? That may have a bearing on this. You can find the sub-model by doing "About this Mac..."
1) Shine a bright light into the audio-out jack and look for dust bunnies or other debris
2) Can you correlate the balance issue with the rotational position of the headphone plug? Try turning the plug right and left while listening and see if the sound changes while turning. It won't fix anything but t can add a clue to the collection of symptoms.
3) Also see if it varies with how far you inset the plug. Insert the plug slowly until you just hear sound with separation and stop. Now slowly continue inserting until it cannot go farther. Does the sound lever or the separation quality change?
The third test looks for an problem I thought was history but, who knows. That problem in the past was ultimately due to analog plugs not playing well in Macs' digital audio jack. Apparently, even good analog plugs were not built to the same precision as the digital jacks Apple installed. Again, that is a long shot today but easy to check.
I agree that the fact that this does not happen with wireless headphones suggests a hardware issue.
