The wighted fractional count (WFC) is a modified version of FC in which fractional counts for articles from specialist astronomy and astrophysics journals have been down weighted. These journals encompass a much larger proportion of the total publication output of these fields than any other field covered by the Nature Index. The WFC allows ordering of institutions and countries so as not to give undue emphasis to these fields. The weighting is achieved by multiplying the fractional count from these astronomy and astrophysics journals by a factor of 0.2. This down weighting is in proportion to an approximation of the level to which astronomy and astrophysics articles are overrepresented compared to the total publication output of other fields covered by the Nature Index.