Thanks - that seems to be the fastest possibility. I wrote the functions for Dataset and DataArray

``` python def average_da(self, dim=None, weights=None): """ weighted average for DataArrays

Parameters
----------
dim : str or sequence of str, optional
    Dimension(s) over which to apply average.
weights : DataArray
    weights to apply. Shape must be broadcastable to shape of self.

Returns
-------
reduced : DataArray
    New DataArray with average applied to its data and the indicated
    dimension(s) removed.

"""

if weights is None:
    return self.mean(dim)
else:
    if not isinstance(weights, xray.DataArray):
        raise ValueError("weights must be a DataArray")

    # if NaNs are present, we need individual weights
    if self.notnull().any():
        total_weights = weights.where(self.notnull()).sum(dim=dim)
    else:
        total_weights = weights.sum(dim)

    return (self * weights).sum(dim) / total_weights

-----------------------------------------------------------------------------

def average_ds(self, dim=None, weights=None): """ weighted average for Datasets

Parameters
----------
dim : str or sequence of str, optional
    Dimension(s) over which to apply average.
weights : DataArray
    weights to apply. Shape must be broadcastable to shape of data.

Returns
-------
reduced : Dataset
    New Dataset with average applied to its data and the indicated
    dimension(s) removed.

"""

if weights is None:
    return self.mean(dim)
else:
    return self.apply(average_da, dim=dim, weights=weights)

```

They can be combined to one function:

``` python def average(data, dim=None, weights=None): """ weighted average for xray objects

Parameters
----------
data : Dataset or DataArray
    the xray object to average over
dim : str or sequence of str, optional
    Dimension(s) over which to apply average.
weights : DataArray
    weights to apply. Shape must be broadcastable to shape of data.

Returns
-------
reduced : Dataset or DataArray
    New xray object with average applied to its data and the indicated
    dimension(s) removed.

"""

if isinstance(data, xray.Dataset):
    return average_ds(data, dim, weights)
elif isinstance(data, xray.DataArray):
    return average_da(data, dim, weights)
else:
    raise ValueError("date must be an xray Dataset or DataArray")

```

Or a monkey patch:

python xray.DataArray.average = average_da xray.Dataset.average = average_ds