I read the readme.txt file of Archives for a category WordPress plugin.
The plugin author has stated following limitation on it.
This plugin does not work for weekly archives. The list with archive links is correct, but the
links themselves do not include the category. So when used, WordPress will not filter the resulting
page on the category.
The technical reason is that WordPress does not apply filters when the links for weekly archives
are generated, so the plugin can't change them. Perhaps this is fixed in a next version of
I checked latest version of wordpress(3.5.1) to find out whether this version has added any filter for weekly url but it has not added yet :(
I think you will have to develop custom code and sql query to implement this functionality and should not depend on Archives for a category WordPress plugin and wp_get_archives function to implement this functionality.