Have a look in the install and setup guide 
If vCenter Server, vCenter Single Sign On and vCenter Inventory Service are installed on the same host machine (as with vCenter Simple Install), 10GB of RAM are required. |
Memory requirements are higher if the vCenter Server database or vCenter Single Sign On database runs on the same machine as vCenter Server.
Same page, another GB for the vSphere Client and 2 GB for Web Client.
So you could say the minimum requirement would be around 12 GB RAM to be supported.
As to why, Java tomcat eats up quite some memory. Single Sign On, Inventory Service, vCenter Management Web Services, Web Client are all tomcat processes.