Both verbs seem to mean the same thing: "to give support to someone or something". Is there any difference between the verbs?
Also, are there any cases which I can't use "to back (up)" instead of "to support"?
To "back" someone or something means to support it.
She backed the ban on WMD.
To "back up" means to be available to substitute for someone or something.
He was backing up our normal delivery man who was out on medical leave.