Hi peter
I can't give a direct lead, but here are some thoughts.
If it is a really top quality piece it might even be worth sending it to the UK or USA. Polishing is going to cost anywhere from £25 to £60, depending upon the nature and degree of damage, plus extra if it needs facetting or a concave base cleaning up - and it is rarely a quick operation! Antique paperweights made of lead glass are softer, easier to polish, and bruises tend to be shallower.
Modern weights are usually harder, and particulary in the case of earlier Paul Ysart weights, more prone to cracking during polishing if there is any latent damage. Hertzian ring cracks, if you will pardon the technical term, are not always visible to the naked eye, and can reveal themselves on polishing: a weight that has 'just the odd scratch' can reveal significant bruises beneath the scratch, or elsewhere, once the surface is disturbed.
It is also worth checking whether the polisher uses water lubricated diamond belts - which tend to run cooler - rather than cork / cloth / felt mops, as the heat of the latter can occasionally cause stress fractures.
Hope this helps
Alan