[BUG] `np.average` with weights fails

import numpy_quaddtype
x=numpy_quaddtype.QuadPrecision([1,2,3])
y=numpy_quaddtype.QuadPrecision([2,2.5,2.3])
np.average(x,weights=1/y)

fails:

File ~/miniforge3/envs/pintdev_arm/lib/python3.14/site-packages/numpy/lib/_function_base_impl.py:587, in average(a, axis, weights, returned, keepdims)
    584 else:
    585     result_dtype = np.result_type(a.dtype, wgt.dtype)
--> 587 scl = wgt.sum(axis=axis, dtype=result_dtype, **keepdims_kw)
    588 if np.any(scl == 0.0):
    589     raise ZeroDivisionError(
    590         "Weights sum to zero, can't be normalized")

File ~/miniforge3/envs/pintdev_arm/lib/python3.14/site-packages/numpy/_core/_methods.py:49, in _sum(a, axis, dtype, out, keepdims, initial, where)
     47 def _sum(a, axis=None, dtype=None, out=None, keepdims=False,
     48          initial=_NoValue, where=True):
---> 49     return umr_sum(a, axis, dtype, out, keepdims, initial, where)

TypeError: Cannot pass a new user DType instance to the `dtype` or `signature` arguments of ufuncs. Pass the DType class instead.

Without the weights argument this works OK.

Start by reproducing the provided weighted np.average example with numpy_quaddtype. Inspect the weighted path around NumPy's average implementation and dtype handling shown in the traceback. Done means the example no longer raises the new user DType instance error while preserving the existing unweighted behavior.