The issue here is that whatever weight material I am using (whether it's copper-coated bbs, glass beads, etc) tends to get stuck on the fibers of the cloth, inside of the channel. The reason for the extra tubing is for ease of insertion.Since your fabric already has "tubes", how about eliminating the extra "tubing" and select the weight diameter to match the fabric tubes.
Some of them are uniform, some of them aren't. My simplest designs involve uniform channels that I fill and then sew seams to separate into individual compartments.p.s. that assumes of course that the sewing is uniform ... hmm maybe use gravel