From what I've read, Columbia and NYU brag about having mature applicants with years of work experience and grad degrees. So I imagine they love WE and grad degrees.
Diversity seems to help in most LS not just columbia and nyu.
But to say how much these things help would be just conjecture.
There seems to be nothing stronger than URM (outside of the #s).
When it comes to it. Yes it is just a #s game. The extras help but probably to a small degree (except for URM).
Probably best to contact the schools themselves and ask how they value extras like WE, EC, PS, and grad degrees.