Ross Kirsling's D3.js-based [Directed Graph Editor](http://bl.ocks.org/rkirsling/5001347) is a simple and convenient point-and-click online graph editor.  It doesn't include weighted edges, but it probably wouldn't be difficult to add that capability if you're willing to learn D3.js.  (Learning D3.js's weird conceptual model is not necessarily a trivial project, even for experienced programmers).  

Kirsling's graph editor is not very smart about layout (although that might be fixable), is not designed to load data (although that's easy to add in D3.js), and it lacks other fancy features that some of the tools listed here include.  However, it's right there online, and it might be one all needs for some purposes.  

Kirsling's graph editor is part of his [Modal Logic Playground](http://rkirsling.github.io/modallogic).