I have found a way around this problem for warps that aren’t very long – say under 5 yds. I don’t wind separate warps any longer and wind both warps together for all my double weave and for supplementary warp projects.
After I have the loom threaded and tensioned at the front, I weave until I find that there is a tension difference between the 2 layers, in many fabrics this never happens, especially when both warps are made of the same material. However, in other warps where there is a take-up issue, ie supplementary warps or say one warp is stretching more than the other and needs more tension, I have learned to handle it a simpler way. I raise the harnesses that hold all the threads that need more tension and I separate that layer from the base layer by sliding a rod under that portion of the warp (this is all taking place behind the harnesses). I then release the tension at the front of the loom so I can slide the freshly inserted rod over the thread beam so that it is hanging at the base of the warp beam. Then I put on 3 S hooks on the rod, one on each end and one in the middle and put identical weights on them (whatever you need to take up the difference). Go back to the front of the loom and re-tension. Weave away and you will find that when you release tension to advance your warp the rod just keeps sliding down and both warps re-tension exactly the same.
It is pretty cool and I do this now on all my looms regardless of 2 beams, 1 beam, 2 brakes, 1 brake ………… doesn’t matter. I read about this years ago in an Ann Sutton book that is no longer in print. It works like a charm.