This functionality is available to Administrators only.

1. Adding a weight field to the page type:

Structure->Content Types->Basic Page/Article->Manage Fields

Now you want to add a new field under Category Tags:

Make that it is an Integer.

Next save through the next two windows as you most likely don't want to change many if any of the settings. 

2. Hide the field on the page.

Structure->Content Types->Basic Page/Article->Manage Display 

Drag the Sorting Weight field under the hidden label and save.

3. Add the weightings to the pages required. 

4. Adding the sort by weight to your view of choice. 

Structure->Views->your view of choice

Then you want to remove everything from the sort criteria panel list and just add Sorting Weight.

Now your view should display the items in the order for which you weighted them.