Weighted quantile calculation is incorrect

What happened?

DataArrayWeighted.quantile returns incorrect numbers for weighted quantiles.

As an example, passing a quantile of 1 should return the maximum value by definition, but when there are weights, it will oftentimes return a different number.

What did you expect to happen?

A quantile of 1 should return the maximum value. Note that the calculation is also incorrect for lower quantiles, not just for q=1.

Minimal Complete Verifiable Example

import numpy as np
import xarray

(
    xarray.DataArray(
        np.array([1,10,100])
    )
    .weighted(
        xarray.DataArray(
            np.array([10,10,5])
        )
    )
    .quantile(
        1.
    )
    .to_numpy()
)

array(60.)

MVCE confirmation

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

Start at the DataArrayWeighted.quantile entry point and reproduce the issue with the minimal Python example using the provided values and weights. Check the weighted quantile behavior for q=1 and lower quantiles, then add or update coverage so q=1 returns the maximum and the other quantiles return correct values.