As with all things, workmanship, quality of detail, complexity and at times simplicity, good design, artistic flair, originality.
Value gives a good indication of: Classics age and condition, 20th Century Factory mostly design/skill, Art - a recognised and collected artist.
Personal interest - where you simply collect from the heart and the piece works for you.
Paperweights remain a rich area of discovery as while collectors are amongst the most animated and active of all glass collectors with many very active societies, lots of well researched books, outside of the world of weight collectors the gems are simply unrecognised as being more than a bauble.
Obviously weights (mostly) rely on the clarity of the glass - as a result this is one area that you will find more restored pieces than in any other glass area. Restorations being a complete polish, addition of facets to eliminate chips, partial polishing. How these affect value differs greatly according to rarity and quality of the restoration.
Paperweights are often a team effort and attribution is usually going to the designer of company weights, the canes may have been made by one or more of the workers, lampwork by another, the weight itself by another and any cutting by yet another. Someone else doing any final finishing. Studio makers might buy in canes or make everything themselves.
Techniques, there are dozens of techniques that are employed in paperweights which also makes them an interesting field of study.