In OS 9, the Mac knew what application to open when you opened a file because of "type" and "creator" codes. This system allowed the Mac not to have to use .*** extensions in the file names--which I liked. The file would also take on the icon of a file used by a specific application (or a specific icon for files of that app). The way it worked was that the type code told the computer what kind of file you were working with, such as "ttxt" for text, or "jpeg" for .jpg, which also included one for an application, one for the finder, etc., etc. Each file and app in OS 9 have a type code associated with it. Also, each file and app have a creator code, which is also a four-character figure, which in this case tells the computer what application each file belongs to, so Photoshop had some code (which I don't remember) that let's pretend was "PHSP." All pictures that you saved in Photoshop would automatically take on the creator code of "PHSP," such that the next time you double clicked the picture, Photoshop would open and then open the picture file.
Move ahead to OS X. Files created in Cocoa don't have type or creator codes. Because OS X is based on Unix, files made in Cocoa use extensions after the filename, just like dos and windows. It is not limited to just three characters, but generally will follow that model. If you double click a file, OS X first looks for type and creator codes and follows that paradigm if it finds them. If not, it looks for the .*** extension and opens the program set up to run that particular extension.
For cleanliness sake, and to keep the same OS 9 type experience going, OS X is automatically set up to hide the extension files in the file name (unless you manually type the file name and include the extension as part of the name). You generally don't need to see them as the icons will give away what kind of files they are.
Every once in a while, the Mac gets a little screwed up, such that the usual double-clicking opens the wrong application or no app at all, but instead you get the "what app do you want to open this file with" dialogue. You can then choose an app for that specific opening, but it won't reassign all files with that extension to that app.
To permantly tell the Mac which app to open specific extensions, you need to highlight a specific file of the type you want to assign (in your case .sitx), then go to File->Get Info (or Command-I). Now, make sure the Open With triangle is pointing downward. Using the pop-up menu, tell the computer what application you want to open that particular extension file with from now on (in your case Stuffit Expander), then click the button Change All. Click Continue and voila it is done. All .sitx files from now on will automatically unstuff with Stuffit Expander when double clicked. The default behavior is for the unstuffed file to show up in the same folder as the .sitx file, but you can go into Stuffit and change it to your desktop, or any other place that you want.
Now, there is almost certainly some software available to simply list all the possible extensions and their assigned applications, such that you could easily edit the list and reassign to your hearts content, but I haven't needed such an application yet, so I don't know what it would be.
