You have the heap set to 2GB. The JVM will reserve that memory immediately, but will not start using it until it needs it. That would expalin the RSS increasing - as the app runs and it uses the heap the JVM will start to make use of some of that memory that it has allocated and the OS will make it resident. Notice that after the app has been runnign for a while that the RSS rmains fairly constant.
Note that the VSZ remain fairly constant. The increase after the initial size can be attributed to the perm gen increasing as classes are loaded.
I don't see anything here that would cause me alarm.
As far as what each of the threads are doing, you could take a JVM thread dump and see.