There are three reasons that RapidWeaver might not be able to install Stacks when it is double clicked:
You double-clicked on the RapidWeaver 6 version of Stacks (Stacks.rapidweaverplugin) but you have RapidWeaver 5 open.
Your Mac will always attempt to open a document with the apps that are currently open first. RapidWeaver 5 will try, and fail, to open files ending with .rapidweaverplugin and vice versa.
Solution: Quit all copies of RapidWeaver before double clicking on Stacks.
You don't have the needed version of RapidWeaver installed.
It could be you are double clicking on a RapidWeaver 6 plugin (like Stacks.rapidweaverplugin), but only have RapidWeaver 5 installed. Or vice versa.
Solution: Download the and install the RapidWeaver 6 version of the plugin (or vice versa).
RapidWeaver is not installed properly on your Mac
Once applications are installed in the Applications folder on your Mac and have been run at least once, your Mac can associate that application with the files it knows how to open. If you have not yet installed or run RapidWeaver yet, then your Mac will not know how to install Stacks.
Solution: Install RapidWeaver and run it at least once.