I would like to be able to specify a "weight" for the article nodes published in the homepage. What is the best way to do this?
You could for example use Nodequeue to create fixed list of nodes and then show that as the front page (as a view I guess).
Or, you could define your own weight field (for example a simple integer field, or a select with options from -50 to 50) and then create a view of nodes which you sort based on that field.
Both Draggeble Views and Nodequeue are great for creating easy-to-use admin pages with drag-and-drop sorting. The main difference between Draggable Views and Nodequeue is that Nodequeue allows manual sorting and selection, whereas Draggable Views allows manual sorting of an automatically populated list (a view). Both modules are explained and compared in these two blog posts.