Edge Inspect is for previewing and inspecting your pages on devices, yes.
Are you using multiple media queries in one stylesheet? If so, this thread may help you work around this issue with weinre:
Just voted on the Apache site, doesn't appear to be exactly the issue as I am getting no CSS at all apart from stuff relating to mobile.safari class. I have several linked files, and only one uses @media queries. Several are linked using @import to ensure they load in the right order. Is it possible @import is also not supported in Weinre?
That's entirely possible, we had another Edge Inspect user ask about that: http://forums.adobe.com/thread/1165285
I'd suggest following up with this thread (yours?) https://groups.google.com/forum/?fromgroups=#!topic/weinre/hgxYmbBXb4M on the weinre forums and getting Patrick the information he requested. In my experience he's very responsive to issues with weinre and by far more experienced at fixing problems with it. If this is a bug rather than a fact-of-life we ought to be able to get his fix into our weinre instance shortly after he posts it.