Your OS and hardware must be 64 bit for this to work.
The only difference between 32 bit and 64 bit webNetwork install are the JRE (Java) files.
Shut down webNetwork
Backup old stoneware system ( c:\stoneware or /usr/stoneware )
Install 64 bit webNetwork on the box or different box in a temp directory like c:\temp\sw64 or /tmp/sw64
Replace the existing c:\stoneware\jre with the jre from the 64 bit install (c:\temp\sw64\jre)
Restore from backup :
c:\stoneware\jre\lib\security\cacerts file.
c:\stoneware\jre\lib\ext directory.
Delete the c:\temp\sw64 direcotry.
Start webNetwork back up.
*It is not recommended to do this process any other way because you need to ensure that you are not mixing and matching the core stoneware files with newer / older versions. Swapping out the JRE per these instructions is the best way to convert from 32 to 64 bit.
**If you are doing an upgrade to 6.1, and are running 32b bit webNetwork on a 64 bit OS, you can just run the 64 bit installer for 6.1. You will automatically be converted to the 64 bit version of webNetwork during the upgrade, without needing to go through all the above steps.