I had a situation last year in which my flight to RNO was diverted to SAC due to weather (although it was delayed in LAX due to mechanical and probably would not have been diverted had it departed on time). Long story short, I stayed overnight at SAC and then rented a car to get to RNO.

AA's rules are pretty clear that they will not reimburse for weather related delays. Rather than fighting city hall, i realized that my credit card had "trip interruption insurance" and filed a claim with the credit card company. It required a bunch of documentation (including an official email from AA stating that the flight was diverted due to weather) but once I filed all the documentation I got reimbursed in a couple weeks. it was actually a pretty painless process as everything could be done online.

You might want to check and see if you have similar coverage on whatever credit card you used for your ticket.