don't apply `weighted`, `groupby`, etc. to `DataArray` without `dims`?

What is your issue?

Applying e.g. ds.weighted(weights).mean() applies the operation over all DataArray objects - even if they don't have the dimensions over which it is applied (or is a scalar variable). I don't think this is wanted.

import xarray as xr

air = xr.tutorial.open_dataset("air_temperature")
air.attrs = {}

# add variable without dims
air["foo"] = 5

print("resample")
print(air.resample(time="MS").mean(dim="time").foo.dims)

print("groupby")
print(air.groupby("time.year").mean(dim="time").foo.dims)

print("weighted")
print(air.weighted(weights=air.time.dt.year).mean("lat").foo.dims)

print("where")
print(air.where(air.air > 5).foo.dims)

Results

resample
('time',)
groupby
('year',)
weighted
('time',)

Related #6952 - I am sure there are other issues, but couldn't find them quickly...

rolling and coarsen don't seem to do this.

Start by running the provided reproduction against the Dataset operations resample, groupby, weighted, and where, checking the dimensions of the scalar foo variable. Compare these results with rolling and coarsen, then determine the consistent expected behavior for variables without the requested dimensions. Done means the affected operations no longer add those dimensions to scalar or otherwise unrelated DataArrays, with regression coverage for the demonstrated cases.