Q. Is there a reason for the number and variant width of black stripes on a taalis? Why are they not placed on a cotton taalis koton?

A. See question 1507 above, where we wrote that some maintain that the black stripes on the taalis represent the retzuos or straps of the tefilin. Therefore some explain that there is seven stripes, since they represent the seven turns of the retzuos there is on the hand, when one wears tefilin. Horav Yaakov Hirshman Shlit’a added that the stripes relate to the seven true ribs of the human body.
Horav Shlomo Miller’s Shlit’a opinion is that the taalis katan since it is usually covered, there may be more leniency in regards to placing the stripes, especially on non-woolen material.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a