id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
2064544219,I_kwDOAMm_X857DnHb,8583,Unexpected Dataset aggregation behavior when weighting,3169620,open,0,,,1,2024-01-03T19:32:11Z,2024-01-04T19:12:58Z,,CONTRIBUTOR,,,,"### 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

```Python
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](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), 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

<details>


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

</details>
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282964952,MDU6SXNzdWUyODI5NjQ5NTI=,1790,'Cookbook' page,3169620,open,0,,,6,2017-12-18T17:46:25Z,2019-12-08T23:31:08Z,,CONTRIBUTOR,,,,"Would there be interest in adding a 'cookbook' section to the docs a-la [Pandas](http://pandas.pydata.org/pandas-docs/stable/cookbook.html)? The current Recipes section might then be better renamed as Gallery?

It's useful for the kind of thing which isn't a full-fledged example, but might be useful nonetheless. I'll hapily put together a pull-request if there's interest. ","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/1790/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,issue