The weights are tapered to fit the horn and attach securely without causing damage. Smaller weights are for use on smaller horns or horns that need only minor adjustment. They work well on yearlings with healthy solid horns. Used on younger cattle, or animals with weak horns, a weight could cause the outer shell of the horn to come off. As a result, the animal's two horns will never match.
Larger weights are for use on larger horns or on cattle whose horns require drastic changes.
To change the horn shape of a mature ox, you must leave the horn weight on for a long time. A more appropriate way to reshape such horns may be by shaving. I have never tried this technique, but I know it works since I have seen many teams with horns that have been shaped this way. If you wish to make a horn more upright, shave the back side. If you wish to widen the span, shave the insides of both horns.