How to sort content in Views by menu weight
1: Referencing a user contributed module: Views menu sort which at #48 has a D7 version. I have not tested this but others report success.

2: Another method you could use is to use a PHP field in your view like in this article on tappetyclick.com. (I have used this method before)

3: Or you can use the module menu node views which requires menu node.