A flyweight is an object that minimizes memory use by sharing as much data as possible with other similar objects; it is a way to use objects in large numbers when a simple repeated representation would use an unacceptable amount of memory.
On the face of it, this patterns looks very much like something from the old ages. And indeed, most implementations of Flyweight are actually focused deeply on low memory conditions. I would actually argue that you need to consider very carefully when you want to do that.
That said, it is actually used fairly often in high performance places. In the .NET framework, the notion of string interning is one way to get flywieghts (although the problem is that you need to start with a string to get the intern string sort of mess things up). In both the profilers and in RavenDB, we have used variations on the Flyweight pattern.
In the profiler, we are mostly dealing with parsing data from the profiled system, and that means doing a lot of reading from a stream and creating objects. That created an unacceptable memory pressure on the system. We implemented a fairly complex system where we can read from the stream into a buffer, then get or create the string from it. We contributed the implementation back to the Protocol Buffers project. You can see the code here.
In RavenDB, we deal a lot with documents, and many times we find it useful to be caching a document. The problem with doing that is that you need to return something from the cache, which means that you have to return something mutable. Instead of copying all of the data all the time, the internal RavenDB data structures supports copy-on-write semantics, which means that we can easily create clones at basically no cost.
Recommendation: If you are in a perf optimization mode, and you worry about memory pressure, consider using this. Otherwise, like all optimizations, it should be left alone until you have profiler results that says you should consider this.