I have only been weaving for three years and am fascinated with doubleweave. I wove a scarf in 3-block doubleweave on twelve shafts. When I finished the scarf, I thought it felt somewhat stiff. Should I have a looser sett or a gentler beat or both? It occurred to me that with multiple layers each layer gets beaten multiple times which caused me to wonder if I should be doing something different with setts and beats as I add more layers and blocks.
Determining the right sett is sometimes tricky. There are many variables, so rules of thumb are only starting points. The starting point for a doubleweave would be to sett the cloth at twice the sett for a single layer. However, many other variables apply. For a sturdy table runner with a plain-weave base in 10/2 pearl cotton, for example, the recommended sett might be 48 ends per inch (twice the single-layer sett of 24 ends per inch). However, if you have a light-weight loom or a table loom or you are weaving a very wide piece, you may not be able to beat hard enough to achieve 48 picks per inch. In that case, you would open the sett to 40 ends and picks per inch.
Important considerations are the yarns you are using and the desired hand of the finished fabric. If you consult the Master Yarn Chart for cotton yarns, the setts are reliable (use the middle number for the sett for a balanced firm plain weave). But for wool yarns, the setts must be considered suggestions only. The degree of spin, the actual specific wool (merino, etc.), the finishing technique, and the desired finished hand are all important variables. Silks, too, vary in the degree of spin. The only way to determine the appropriate sett for these yarns is to sample and finish the sample to check the resulting fabric hand. I always do sampling on the full warp for the intended piece and change the sett after cutting off and finishing a sample.
For your silk scarf, I wonder if you had wet-finished it before judging its stiffness. Silk softens after wet-finishing. Somewhere I learned that you should slap the silk piece against a table or counter after it is dry to further soften the yarns.
At any rate, the additional beating would not be a factor unless you are beating too firmly. To check this, count the picks per inch and make sure you are weaving the intended design to square.