Java heap space error, already at limit of 32-bit JVM?

After doing a lot of SOAP testing today and not experiencing any of the above behaviors, I'm starting to believe these problems are exclusive to REST test requests. We're using identical data structures and loops in the validation steps on the SOAP side of things, but those tests don't seem to be affected by the gradual ramp-up in the memory log.

I'll fire off some heap dump links to the email you provided. Screenshots of memory log behavior on REST vs. SOAP are probably next. Thanks for your help.