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Hi. There are some 'purists' who feel a paperweight should never be 'restored', but I think that overlooks the fact that even the manufacturers occasionally had to polish out minor damage, or facet a piece to remove an air bubble or piece of cullet / pot stone they did not like. For me it is a matter of judgement - would it improve your appreciation of the piece?
Regarding damage, Kevin is correct (in spades) about damage going deeper than it appears - a typical bruise creates damage at least as deep as the diameter, even though it may not appear so at first sight. (Part of my D Phil / post doc work involved both the practice and theory of polishing diamonds, and Hertzian cracks in diamond. If you want to go into the science of this kind of damage, and are feeling strong, Google 'Hertzian cone crack').
Kevin makes another very important point too - removing a significant amount of glass without proper understanding of the shape and the optics can lead to a distortion of the design. You will come across quite a lot of antique pieces where the shape has been changed so that the outer canes have vanished (either in part or fully) when viewed from above. Another fault you will come across are paperweights repolished without the requisite level of skill, using flat wheels or 'scaifes': this can result in lots of little polished flats, hard to spot in an image but easy to feel - and easy to detect when you move the paperweight around in your hand, and the design appears blurred!
Alan