Based on the information we have, which is imperfect to be sure, we
believe this is caused by a Firefox bug,
https://bugzilla.mozilla.org/show_bug.cgi?id=638075
The short version is that Firebug is monitoring net traffic because
this net traffic comes before we know if you want to use it in
debugging or not. Once we look at the traffic we cannot stop
accumulating data because of the Firefox bug. The common case where
people see this is to have firebug installed in a browser that they
also use to access large resources like video.
You can run two copies of Firefox using -no-remote and in one copy
have a profile with only debug tools. In that copy you don't watch
videos and in the other copy you don't install Firebug.
jjb