The law deals with this in a variety of ways. In contract law, you can have liquidated damages clauses that set a financial penalty for failure to meet the terms of the contract. In tort law, we have class actions (that allow aggregation of minor injuries into one action) and punative damages. In copyright (and other stautory rights), we have stautory damages.
Under the copyright law, you need not prove that you actually suffered injury from copying to receive a monetary award. There are good reasons for this. Any individual act of copying will have a minor cost, but in the aggregate will cause significant harm to the rights holder. The rights holder may not be able to prove precisely how many sales the availability of the infringing work prevented. Finally, we wish to deter people from violating the copyright law.
In contract and tort law, however, it is a well established principle that the award must still bear some realtionship to the actual or potential cost of the injury. In tort law in particular, recent Supeme Court jurisprudence has set limits on punitive damages under the Constitutional prohibition on excessive fines.
A number of academics have argued that the same logic applies (perhaps even more forcefully) to excessive statutory damages in copyright. As reported here, http://www.betanews.com/article/RIAA_Piracy_Damages_Questioned_in_Ruling/1163182272, a federal district court judge in NY has allowed a defendant in a copyright suit to persue this argument against a $750 statutory damages claim for downloading a single song, available from a legal downloading website for almost 1/1000th of that.
As Judge Tragger is careful to point out, he takes no position at this stage on the merits of the argument presented by the defendant. Rather, he holds that the defendant has submitted sufficient legal argument that the proposed legal defense is not frivilous, and she may therefore present further argument and evidence in support of the claim that the statutory damages proposed are unconstitutional.
Could be an important case to watch.