A suite of Matlab codes written to analyse animal social organisation and structure based on association data, has now a module to analyse weighted networks (including randomisation analyses, community structure, etc...).
(you can find a link to the manual at the bottom of the page).
It is free to download, but of course you need a version of Matlab and its statistics toolbox. There is an experimental compiled version though, which should work without the full version of Matlab. I am hoping in the near future that we will be able to move it to Octave so that the program is truly freely available.
There is also an exporting function to get the data to a drawing software. After looking at many of the different format available we went for .vna (used with Netdraw) because it was simple and versatile (ie, easy to translate into another format if need be and easy to add attributes). But this can be changed easily.