Currently, weights throws an error whenever it encounters non-finite values: ArgumentError: weights cannot contain Inf or NaN values. That's highly surprising IMO, basically all other operations propagate NaNs and allow Infs – both basic arithmetics and aggregations.

# totally sensible and unambiguous results:
julia> median([1,2,3,Inf])
2.5
julia> mean([1,2,3,Inf])
Inf
julia> mean([1,2,3,Inf], weights([1,1,1,1]))
Inf

julia> mean([1,2,3,NaN])
NaN
julia> median([1,2,3,NaN])
NaN

# and suddenly:
julia> mean([1,2,3,4], weights([1,1,Inf,1]))
ERROR: ArgumentError: weights cannot contain Inf or NaN values
julia> mean([1,2,3,4], weights([1,1,NaN,1]))
ERROR: ArgumentError: weights cannot contain Inf or NaN values

I looked up as found that this error was introduced after the issue #671. I think throwing this exception denies perfectly sensible behavior, so that weighted aggregations worked exactly as their unweighted counterparts – by propagating NaNs. And the throw in weights() should be removed, maybe adding it in specific aggregations where Infs/NaNs really do not make any sense (eg, mean and median should work).

Numpy does propagate, of course:

In [2]: np.average([1,2,3], weights=[1,np.nan,3])
Out[2]: nan