It seems the font weight: 400 is bolder than 600. Does this happen only to me? On my Mac Book Pro, it displays the same on Chrome, Safari and Firefox. So, I guess it is not a browser related issue.
https://www.google.com/fonts#UsePlace:use/Collection:Source+Sans+Pro
What is the best solution for this? Using font weight:600 rather than 400 for a normal font weight? I don't know how to report the issue to Google.
As mentioned in the comments, this is likely an issue with your machine (happens to the best of us).
Take a look at this fiddle on a different machine (I've personally verified font-weight changes on multiple browsers); you will see the differences.