How can I add a "weight" functionality to nodes? 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.