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
437765416,MDExOlB1bGxSZXF1ZXN0MjczOTcxOTQy,2922,Feature/weighted,10194086,closed,0,,,22,2019-04-26T17:09:02Z,2021-02-03T14:47:52Z,2020-03-19T14:29:43Z,MEMBER,,0,pydata/xarray/pulls/2922," - [X] Closes #422
 - [X] Tests added
 - [X] Fully documented, including `whats-new.rst` for all changes and `api.rst` for new API

I took a shot at the weighted function - I added a `DataArrayWeighted` class, that currently only implements `mean`. So, there is still quite a bit missing (e.g. `DatasetWeighted`), but let me know what you think.

``` python
import numpy as np
import xarray as xr
da = xr.DataArray([1, 2])
weights = xr.DataArray([4, 6])
da.weighted(weights).mean()

# <xarray.DataArray ()>
# array(1.6)
```

There are quite a number of difficult edge cases with invalid data, that can be discussed. 

* I decided to replace all `NaN` in the `weights` with `0`.
 * if weights sum to `0` it returns `NaN` (and not `inf`)
``` python
weights = xr.DataArray([0, 0])
da.weighted(weights).mean()
```
 * The following returns `NaN` (could be `1`)
``` python
da = xr.DataArray([1, np.nan])
weights = xr.DataArray([1, 0])
da.weighted(weights).mean(skipna=False)
```

It could be good to add all edge-case logic to a separate function but I am not sure if this is possible...
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