The webrep has very little to do with security, it isn't scanning anything, when you visit a site it checks that domain against the avast database for its reputation, etc. So as far as CPU and RAM goes this should be minimal, so I think that in stopping it and the issue stopped is a coincidence.
Whilst browsing the web shield will be using CPU and RAM, but again this isn't displayed in isolation as all shields are controlled by the avastSvc.exe process, so any memory and cpu use would be collated under that.