Just sent this to my VAR but thought I'd let everyone know. I'll post their response when I get it.
Overriding an assembly's mass doesn't work if the assembly is set to be flexible.
Assembly with the weight overriden but not set on flexible:
Assembly with the weight overriden AND set to flexible.
Edit: Forgot to mention, running on SolidWorks 2016 SP4.0. Soon migrating to SolidWorks 2017 SP5.0