href in your CSS is a relative link. So for www.example.com/user the browser will request the css file at www.example.com/webpage.css, but for www.example.com/user/contact it will request www.example.com/user/webpage.css
That may cause part of your problem and can be fixed by preceding your hrefs with a /, so
href="/webpage.css". The / will cause the browser to always request from the root of your domain so it will always request www.example.com/webpage.css regardless of the page you're on. If your css is inside some folder within your DocumentRoot (I assume you're using Apache here), you should be providing the full path to the file from the start of the doc root so possibly something like
In the comments, Michael is also correct that you may have a rewrite rule error so please add that information to your question.