diff --git a/base/reducedim.jl b/base/reducedim.jl
index 27c5e05e40c46..27c1162e7fedb 100644
--- a/base/reducedim.jl
+++ b/base/reducedim.jl
@@ -843,6 +843,12 @@ function _sum!(f, R::AbstractArray, A::AbstractArray{T,N}, w::AbstractArray;
     check_reducedims(R,A)
     reddims = size(R) .!= size(A)
     dim = something(findfirst(reddims), ndims(R)+1)
+    if dim > N
+        dim1 = findfirst(==(1), size(A))
+        if dim1 !== nothing
+            dim = dim1
+        end
+    end
     if findnext(reddims, dim+1) !== nothing
         throw(ArgumentError("reducing over more than one dimension is not supported with weights"))
     end
diff --git a/test/reducedim.jl b/test/reducedim.jl
index a90c2c1f96afb..c8c030d3704ce 100644
--- a/test/reducedim.jl
+++ b/test/reducedim.jl
@@ -482,6 +482,9 @@ end
         end
     end
 
+    # Corner case with a single row
+    @test sum([1 2], weights=[2], dims=1) == [2 4]
+
     @test_throws ArgumentError sum(exp, [1 2], weights=[1, 10], dims=1)
     @test_throws ArgumentError sum([1 2], weights=[1 10], dims=1)
 end
\ No newline at end of file