To check your version of Java, run
java -version
in a console (command prompt). On Windows 7 with 64-bit Java 6 I get:
java version "1.6.0_27"
Java(TM) SE Runtime Environment (build 1.6.0_27-b07)
Java HotSpot(TM) 64-Bit Server VM (build 20.2-b06, mixed mode)
Note the 3rd line, which shows that this is a 64-bit version.
On a 32-bit version you'll get something like:
Java HotSpot(TM) Client VM (build 20.1-b02, mixed mode, sharing)
Check that this is the version being used by Eclipse, as shown in your error code. If not, call that version explicitly, by running the following command in a console (command prompt):
"C:\Program Files (x86)\Java\jre7\bin\java.exe" -version
(using the correct path to java.exe as shown in your error message, not necessarily the path shown in my example above!)