I've discussed this with other developers and now agree that a test should be added.  While the current code's handing of Inf or NaN is correct in a technical sense, it is neither intuitive or useful.

Even though it will have a small time cost for the common case of two weights, we should add a test just after the check for the total being greater than zero:

    if not _isfinite(total):
        raise ValueError('Total of weights must be finite')

Also edit the docs to say:

   Weights are assumed to be non-negative and finite.

Ram, since this was your finding, do you want to make a PR for it (with a test, news entry, and doc edit)?