Why can't I download iOS 7 on my iPhone 3Gs?
You cannot download it because iOS 7 is not supported on any iPhone model prior to the iPhone 4. The latest version of iOS that will run on the 3Gs is iOS 6.1.6 -- which you have.

Here's a fantastic compatibility chart for iOS 7:



Source: http://cdn.theapplelounge.com/wp-content/uploads/2013/06/iOS-7-Comparison-Chart-definitivo-1.jpg

Note the complete absence of the iPhone 3G and 3GS models.