Unexpected Dataset aggregation behavior when weighting

What happened?

When aggregating a dataset over specified dimensions I don't expect variables which don't have those dimensions to be aggregated.

What did you expect to happen?

When a weighting is applied to the aggregation, variables which do not have the aggregation dimensions are nevertheless aggregated. Presumably because the weights get broadcast across those variables. Perhaps this is the intended behavior but it seems surprising to me and should at least be documented I think.

Minimal Complete Verifiable Example

import xarray as xr
import numpy as np

var1 = np.ones((2, 2, 3))

var2 = np.ones((3))

lon = np.arange(4).reshape(2, 2)
lat = np.arange(4).reshape(2, 2)

ds = xr.Dataset(
    {
        "temperature": (["x", "y", "time"], var1),
        "precipitation": (["time"], var2),
    },
    coords={
        "lon": (["x", "y"], lon),
        "lat": (["x", "y"], lat),
        "time": np.arange(3),
    },
)

print(ds.sum(['x', 'y']))
# Precipitation (with no x or y dimension) is not summed over, leading to values [1. 1. 1.]

print(ds.weighted(xr.ones_like(ds['temperature'])).sum(['x', 'y']))
# Precipitation is now summed over, leading to values [4. 4. 4.]

MVCE confirmation

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

Relevant log output

No response

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS ------------------ commit: None python: 3.9.16 | packaged by conda-forge | (main, Feb 1 2023, 21:38:11) [Clang 14.0.6 ] python-bits: 64 OS: Darwin OS-release: 23.1.0 machine: arm64 processor: arm byteorder: little LC_ALL: None LANG: None LOCALE: (None, 'UTF-8') libhdf5: 1.12.2 libnetcdf: 4.9.1 xarray: 2023.3.0 pandas: 1.5.3 numpy: 1.23.5 scipy: 1.10.1 netCDF4: 1.6.3 pydap: None h5netcdf: None h5py: 3.8.0 Nio: None zarr: 2.14.2 cftime: 1.6.2 nc_time_axis: None PseudoNetCDF: None rasterio: 1.3.6 cfgrib: None iris: 3.4.1 bottleneck: None dask: 2023.3.2 distributed: 2023.3.2.1 matplotlib: 3.7.1 cartopy: 0.21.1 seaborn: 0.12.2 numbagg: None fsspec: 2023.10.0 cupy: None pint: None sparse: None flox: None numpy_groupies: None setuptools: 67.6.1 pip: 23.0.1 conda: None pytest: None mypy: None IPython: 8.12.0 sphinx: None

pydata / xarray