Reduction operations fail with Weighted DataArrayWeighted

What happened?

I have a DataSet with some weighted DataArrays. This set-up is extremely useful to me as I can filter and perform operations over the whole dataset and all shared dimensions. One of the DataArrays is weighted, and I was hoping this would be automatically handled in groupbys and general reduction operations, but the error thrown is below. If I call mean on the dataset.

I'm happy to raise a PR to fix if I can work out how to do it, but I just want to make sure that it's agreed that this isn't correct behaviour.

What did you expect to happen?

I would like DataArrays that are unweighted to return the usual mean, and for DataArrayWeighted to return a mean reflecting their weights, as if I'd just called da_weighted.mean(). This would allow me to calculate means in groupbys on the DataSet.

Minimal Complete Verifiable Example

import numpy as np
import xarray as xr

da = xr.DataArray(
    data=[[4.0, 5.0, 6.0], [1.0, 2.0, np.nan], [np.nan, np.nan, np.nan]],
    dims=["t", "x"],
    coords={"t": [0, 1, 2], "x": ["a", "b", "c"]}
)

dw = xr.DataArray(
    data=[0.1, 0.2, 0.3],
    dims=["t"],
    coords={"t": [0, 1, 2]}
)
db = da.copy(deep=True).weighted(dw)
ds = xr.Dataset({"a": da, "b": db, "w": dw})

# This works
print(db.mean())

# Errors
print(ds["b"].mean())

# Errors
print(ds.mean(dim="t"))

# Errors
print(ds.groupby_bins("t", bins=[0, 2.5]).mean())

MVCE confirmation

• Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• Complete example — the example is self-contained, including all data and the text of any traceback.
• Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• New issue — a search of GitHub Issues suggests this is not a duplicate.
• Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

python weighted_demo.py
<xarray.DataArray ()> Size: 8B
array(3.)
Traceback (most recent call last):
  File <redact>, line 22, in <module>
    print(ds["b"].mean())
          ^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/core/_aggregations.py", line 2982, in mean
    return self.reduce(
           ^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/core/dataarray.py", line 3839, in reduce
    var = self.variable.reduce(func, dim, axis, keep_attrs, keepdims, **kwargs)
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/core/variable.py", line 1677, in reduce
    result = super().reduce(
             ^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/namedarray/core.py", line 918, in reduce
    data = func(self.data, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/core/duck_array_ops.py", line 680, in mean
    return _mean(array, axis=axis, skipna=skipna, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/core/duck_array_ops.py", line 447, in f
    return func(values, axis=axis, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/core/nanops.py", line 124, in nanmean
    return _nanmean_ddof_object(0, a, axis=axis, dtype=dtype)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/xarray/core/nanops.py", line 117, in _nanmean_ddof_object
    data = np.sum(value, axis=axis, dtype=dtype, **kwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.py", line 2389, in sum
    return _wrapreduction(
           ^^^^^^^^^^^^^^^
  File "<redact>/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.py", line 86, in _wrapreduction
    return ufunc.reduce(obj, axis, dtype, out, **passkwargs)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
TypeError: float() argument must be a string or a real number, not 'DataArrayWeighted'

Anything else we need to know?

There are several functions that might fall into this category like std, but I think they could all be handled similarly.

Environment

Start with the weighted_demo.py reproduction and trace the reduction path through xarray/core/_aggregations.py, dataarray.py, variable.py, duck_array_ops.py, and nanops.py. Compare Dataset and groupby_bins reductions with DataArrayWeighted.mean; done means unweighted variables retain normal reductions while weighted variables produce weight-aware results, with coverage for mean and related operations.