Do certain recommenders carry more weight than others?

[Sciencewoman]

I think you should be appreciative and positive toward any recent alumnae of chapters at your school -- don't rebuff anyone who actually knows the current actives. They can vouch for you, or just as easily tell their sisters that you said "no, thanks" to a rec offer. If anyone is eagerly offering, take them up on it graciously.

A rec writer who is a high level alumnae officer or a trusted advisor attracts attention, when they're submitted on behalf of PNMs who are well known to the officer.

I wouldn't try to "shop around" for the "best" rec writers -- accept all offers. If you have more than one for a group, that's fine and even common at many competitive campuses.