The JVM you are using is installed in Program Files (x86). This is almost certainly the 32 bit version of the JVM. On a 64 bit system, 64 bit programs are installed in Program Files, 32 bit programs are installed in Program Files (x86). Unless you changed the default when installing the 64 bit version, you are running against the 32 bit version.
You need to either download and install the 64 bit version (If you plan on doing Java development, I would recommend a JDK instead of a JRE), or you need to download the 32 bit version of Eclipse.