Lesson 6 in the Adventures in Weaving on a 2 Harness Loom makes stripes in the warp and weft but these are thicker cloths. How thick depends upon the thicknesses of the weft yarns. Usually the warp yarns are about the size of a thinner yarn. However, all of this can be experimental and just how thick or how thin is the choice of the weaver and whether you want a fabric or a mat or a rug and which colors you want to dominate or recede.
An example of a thick yarn is a rug wool which has 250 yards per pound.
A thin yarn can be 5/2 cotton at 2100 yards per pound.
Notice that in the threading draft, some areas are threaded with 2 colors alternating like in log cabin. Other areas are threaded in all one color.
All the examples in the book are woven with only thick weft yarns. You get a fine stripe in the areas where the warp colors alternate and solid color when only one color is used in a warp stripe.
In my book, Weaving for Beginners, I describe a variation where thick and thin wefts alternate, and 2 colors alternate in the warp. This lets you choose which warp color you want to dominate. You do that by having that color warp threads up when you throw the thick weft. Alternately, when the thin weft passes, the other color will recede. The illustration shows how you can have one or the other dominate as you choose for your design.