I think the bruising that Jan is talking about is caused by the stretching that can be introduced when ripping along the cross grain. In hand weaving it is true that sometimes the warp threads (the long straight of grain threads, the ones mounted on the loom) are stronger than the weft threads. For instance, in rug making this is usually the case. However, it depends on the type of cloth being woven, what it's purpose or end use will be, and what type of weave the weaver is doing. I spent many years weaving and often wove fabrics in which the warp and weft used exactly the same threads.
For commercially woven, quilting cottons, the warp and weft threads are not likely to be different in terms of strength. However, if you will pull on your fabric in the lengthwise (parallel to the selvage) and crosswise, you will note that there is more stretch in the crosswise. This is due to the fact that those threads are not stretched as tightly during the weaving process as are the warp threads which are under tension on the loom. The fact that the weft threads are not under tension when they are woven is what causes distortion when tearing across the grain.
Tearing with the grain (lengthwise, parallel to the selvage) should not cause any fabric distortion if using all cotton fabric and if the weave structure is what is known as a "balanced weave". Other kinds of weave structures can cause distortion when tearing with the grain.
Rob
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