As always you ask a interesting question. The purpose of a sliding weight (if it is indeed functional not decorative) is to move your point of balance down the blade. Essentialy converting a rapier (light blade with a point of balance closer to the hilt) into an axe. As you know the cutting ability has a lot of variables such as edge geometry, draw cut etc. However the sliding weights function would be to add mass to the point of impact thus increasing the kinetic energy which then gets converted into cutting energy. KE=1/2mv2 (kinetic energy = one half mass times the velocity squarded). The amount of mass added will then depend on where your sliding weight is in relation to the point of impact which ideally will be on the point of impact.
As a disclaimer I am not a physicist