I run Windows 7 64-bit. I have the Java JRE 32-bit installed. I use Firefox almost exclusively for web browsing. I see there is a 64-bit JRE, but I can't really tell what use it is. Under what ...

Ideally this is resolved without creating platform-specific Java-GI jar files. The Java bindings can provide the "lowest common denominator", i.e. always use int in Java when the native type is long.