The discussion about how to treat author self-citations driven by policy application and quality measurement intensified in the last years. The definition introduced by Snyder and Bonzi has - in lack of any reasonable alternative - been used in bibliometric practice for science policy purposes. This method, however, does not take into account the weight of self-citing authors among co-authors of both the cited and citing papers. The objective of the present paper is to quantify the weight of self-citations with respect to co-authorship. The analysis is conducted at two levels: at the macro level, namely, for fifteen subject fields and the most active forty countries, and at the meso level, for a set of selected research institutions.