Stretching a piercing is a devotion, a meditation, a test of patience. It must be carried out slowly, as any deliberate modification of the body must be. Stretch too quickly and the piercing will become irritated and begin weeping lymph like a new piercing. A worse case scenario would result in a broken or torn piercing.
Wire thickness is sized much like women's clothing, except that the smaller the number, the larger the gauge. An average earring is 18 or 20 gauge. Any body piercing should be at least 14 gauge before beginning to stretch it, as anything thinner might rip into the surrounding tissue. Initial piercings can be up to 8 gauge, so if you know want really enlarged piercings, start as large as possible. Any metal jewelry should be surgical stainless steel, solid gold (at least 14 karat), or niobium, titanium, or platinum. Heavy monofilament nylon or inert plastic is also tolerable.
There are a few methods for producing a larger piercing. The first is weighting which merely entails hanging a heavier and heavier weight from the piercing. Care must be taken not to hang too much weight from too thin a ring. (Imagine a cheese slicer....) An example of the effect weighting produces can be seen in the Dyak women of Borneo. In their society, the longer the earlobe, the more it corresponds to their ideal of beauty. The lobes are pierced during childhood and progressively larger earrings are worn until a three-quarter inch wooden plug can fit. At this point, metal rings are hung from the lobes. These are slowly added to until the earlobes have stretched down to the collarbone.
If a larger piercing is desired without distending the ear (or other body part), the piercing can be enlarged by wearing progressively thicker jewelry. Many Jewish and Arab tribes women in ancient Afghanistan wore very thick, ornate earrings. The earrings were often attached to a headdress or shawl to support the weight of the jewelry, so the earlobe wouldn't be stretched into a loop.
Piercings can be slowly made larger by using a piece of special equipment called a "taper." This is a slim piece of metal, which is one gauge thickness on one end, and slowly tapers to one size larger by the other end. These can be slowly inserted into body piercings, using lubrication to help the skin friction, and the result is a one size increase. Jewelry of the next size up can then be inserted and piercings stabilized at the new size. Once they heal, the process can be repeated. If a piercing is "sized up" too quickly, the tissues can tear, and the piercing will have to be cared for as if it were brand-new all over again.
To learn more about ear piercing, you can read more about every kind of ear piercing or you might like Body Piercing: A Medical Dictionary, Bibliography, And Annotated Research Guide To Internet References by Icon Health Publications.