Check out and work on gh-4960, it might be pretty much done even, but a couple of extra eyes are probably necessary in any case.

Nvm. you mean var not covariance, but that might have similar problems, at least when you get into ddof != 1, so it would be good to synchronize such decision.

A weighted variance is calculated in exactly the same way as a single-variable weighted covariance.

Weights are available for cov since #4960 has been merged. @MechCoder Check it out. It isn't quite as convenient as the ndarray.var method, but should suffice. In fact, the var method is implemented in numpy/core/_methods.py, so it probably would not be difficult to use bits of the code in #4960 to implement weights. Make a PR if you wish.

Sorry for the non-replying. I shall have a look right now.

I believe the discussion here is similar to #8581, so this can be closed in favor of that issue. Please reopen if this is not the case.