diff --git a/docs/python-api.md b/docs/python-api.md
index ac53d3fce9..a8236daadf 100644
--- a/docs/python-api.md
+++ b/docs/python-api.md
@@ -321,6 +321,7 @@ Single site
       TreeSequence.Fst
       TreeSequence.genealogical_nearest_neighbours
       TreeSequence.genetic_relatedness
+      TreeSequence.genetic_relatedness_weighted
       TreeSequence.general_stat
       TreeSequence.segregating_sites
       TreeSequence.sample_count_stat
diff --git a/docs/stats.md b/docs/stats.md
index 222473b9de..c1a34f937d 100644
--- a/docs/stats.md
+++ b/docs/stats.md
@@ -71,6 +71,7 @@ appears beside the listed method.
     * Multi-way
         * {meth}`~TreeSequence.divergence`
         * {meth}`~TreeSequence.genetic_relatedness`
+          {meth}`~TreeSequence.genetic_relatedness_weighted`
         * {meth}`~TreeSequence.f4`
           {meth}`~TreeSequence.f3`
           {meth}`~TreeSequence.f2`
@@ -590,6 +591,11 @@ and boolean expressions (e.g., {math}`(x > 0)`) are interpreted as 0/1.
   where {math}`m = \frac{1}{n}\sum_{k=1}^n x_k` with {math}`n` the total number
   of samples.
 
+`genetic_relatedness_weighted`
+: {math}`f(w_i, w_j, x_i, x_j) = \frac{1}{2}w_iw_j(x_i - m)(x_j - m)`,
+
+  where {math}`m = \frac{1}{n}\sum_{k=1}^n x_k` with {math}`n` the total number
+  of samples.
 `Y2`
 : {math}`f(x_1, x_2) = \frac{x_1 (n_2 - x_2) (n_2 - x_2 - 1)}{n_1 n_2 (n_2 - 1)}`
 
diff --git a/python/tskit/trees.py b/python/tskit/trees.py
index 36fe147488..f80a245126 100644
--- a/python/tskit/trees.py
+++ b/python/tskit/trees.py
@@ -7705,11 +7705,14 @@ def genetic_relatedness_weighted(
         then the k-th column of output will be
         :math:`\sum_{a,b} W_{ai} W_{bj} C_{ab}`,
         where :math:`W` is the matrix of weights, and :math:`C_{ab}` is the
-        {meth}`.genetic_relatedness` between sample i and sample j.
+        :meth:`genetic_relatedness <.TreeSequence.genetic_relatedness>` between sample
+            a and sample b, summing over all pairs of samples in the tree sequence.
 
         :param numpy.ndarray W: An array of values with one row for each sample and one
             column for each set of weights.
-        :param list indexes: A list of 2-tuples, or None.
+        :param list indexes: A list of 2-tuples, or None (default). Note that if
+            indexes = None, then W must have exactly two columns and this is equivalent
+            to indexes = [(0,1)].
         :param list windows: An increasing list of breakpoints between the windows
             to compute the statistic in.
         :param str mode: A string giving the "type" of the statistic to be computed