Right, well I've just tried re-creating what you're seeing and I get the same results.
Database file size within Windows is 301MB, restore selections size for the database is 68MB.
If I select the MSSQL folder within Windows and the SQL server itself for backup, the backup size when SQL Server is running is 2.3GB, however when I stop the SQL Server service the backup size increases to 5GB.
The reason for all this is due to the way that SQL databases are physically larger than the data held within them, allowing them to expand if required when more data is added to them. When you do the backup using the SQL agent then it will backup the SQL data itself, not the physical files, so any empty space will not be included. In fact the physical files are automatically excluded from backup since it knows there's no point since they will be locked. When you do the backup without the SQL agent, then it will backup the physical files completely, including any empty space.
You can see this yourself if you go into SQL Enterprise Manager, and drill down to the database you're referring to. Select the database, and if it's not already displayed switch to the task pad view (right click the database, View, Taskpad), now down at the bottom of the task pad you'll see details of the space allocated, and the space actually used.
I went through all mine and totted up the totals, and found that while the total physical space used by the database files was 4.3GB, the amount of space actually containing data was only 1.6GB, and indeed the data size for the database listed above which was 68MB was correct.
So there you are, another reason for using the SQL agent to backup your databases!
Hope that all makes sense and answers your question.