I am not a tuba player but sometimes a different perspective can be helpful so here 'goes...
When you stand, consider allowing your weight to be delivered down to the ground in cooperation with gravity.
This is different (and perhaps even opposite) of what many music teachers teach. We often hear the tried and true "stand up straight", but what does this mean? It means different things to different people. To some people this means try to make your spine straight and this can cause pain because your spine is not intended to be straight.
The other postural edict which is often issued is ye old "act like a string is pulling you up from your noggin". When I stand like this my entire body is full of tension. If you are subscribing to this, it may be part of your problem.
Your bony structure, including your spine, is designed to hold your body up and to counteract the natural effect of gravity. When you allow this to happen, you need minimal musculature to remain upright. I like to think of this as good balance - when you are balanced around your core, you are not using an inordinate amount of effort just to stand, let alone march with a sousaphone!
When you are balanced, the weight of your torso, arms and head (which can weight the same as a bowling ball!) are delivered right through your massive lumbar core. The five vertebrae which comprise the lumbar portion of your spine are, in fact, massive and will also help you hold up your sousaphone - if you are balanced.
If, on the other hand, you are tucking your butt in an attempt to "stand up straight" the entire idea of balance breaks down and the weight of your torso, arms, head and sousaphone is displaced forward or behind your lumbar core. When this happens, the delicate muscles of your lower back are engaged unnaturally. These muscles were never intended to hold up that much weight - that's what your lumbar core is for.
This entire discussion assumes you have no chronic medical condition. I would not assume this - get things checked out by a doctor and revisit your understanding of posture vs balance...
For more detail, check out my Breathing Book for Tuba
Dave Vining
http://www.mountainpeakmusic.com" target="_blank" target="_blank