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Weight is set such that custom breadcrumbs (node breadcrumbs) are lightest, and path breadcrumbs are heaviest. However, the node type breadcrumbs sometimes override the path ones.
It looks like the call to custom_breadcrumbs_set_breadcrumb in hook_nodeapi is getting run twice.
So, custom_breadcrumbs_set_breadcrumb() runs in node_api then it runs from custom_breadcrumbs_paths_preprocess_page(), which is correct, but then node_api gets called again for some reason, and it gets set back to the breadcrumb defined on the node type.