How do deacons "weigh the needs of causes and use of church resources discerningly?"

Wow, what a great question!  I love that you're engaging with the charge to deacons and have a desire to faithfully live into that calling! 

A good starting place may be found in a resource created by Diaconal Ministries of Canada, it's called  Guidelines for Benevolence.  It's a helpful tool to work through as a deacon team, to get a sense about who you feel called to serve, what your community may need, and how you as a team are equipped to serve.  Having a good idea about who/what God is calling your team to, is part of the discernment process, and may provide you with a starting point as you "weigh the needs".

I'd love to hear thoughts from other deacons on how their deacon boards/teams handle this!

I usually think of "causes" as anything that we can give support to... so, yes, I would consider people as causes for the purpose of understanding the charge to deacons- though I too don't like the word choice - perhaps we can blame it on outdated language!

The denomination has already done some of this work for deacons. See the "Nondenominational Agencies Evaluated for Support 2012" in the booklet at http://www.crcna.org/site_uploads/uploads/Ministry%20Shares%202011%20booklet.pdf.