How many weeks of break (per year) should a graduate student reasonably expect to have?
The official answer depends on where you are located, and the applicable laws in your jurisdiction. For instance, in Germany, graduate students are almost always employees of the government, and are therefore accorded vacation benefits commensurate to that (between 23 and 29 days per year, depending upon age). In contrast, the United States technically does not have any requirements on annual paid leave, so the answer in principle could be as little as zero, but normally is two weeks per year.

Unofficially, that's a matter to be worked out between you and your advisor. Some advisors will be willing to let you take days off here and there as needed, so long as they don't interfere with either your long-term progress or meeting your day-to-day responsibilities. Most advisors will be rightfully displeased if you ask to take two months of leave all at once, but most will not mind a three-day weekend here and there as needed.