I'm really surprised that you're having any issues with just Outlook and web browsing, the Celeron and 2Gb orf RAM should be more than enough to manage this level of usage. Whilst upgrading the memory will undoubtedly help, I can't help thinking that there's a different root cause to your problem - reinforced by your view that it used to be better when you first got your 11z.
I'd be having a good look at the system, checking what processes are running, what dodgy installs you may have inadvertently picked up etc (such as update checkers for programs you rarely use etc). What OS are you running, Vista or Win7?
Have you tried running CCleaner (CCleaner - Optimization and Cleaning - Free Download
): it's really good tool to purge clutter, repair registry entries and lets you easily manage which programs run on startup etc. A defrag of your hard drive often helps too. Perhaps you could also review the antivirus you're running and switching to something with a smaller footprint?
I'd certainly be trying some of these things before I shelled out any more cash.
Just as a reference, I've got a Pentium SU4100 version also with 2GB of RAM and I can have lots of applications open simultaneously including video, firefox with multiple tabs, outlook, etc etc with no performance probs. Even on my old original Asus EEE 4G (much lower spec than your 11z) I was able to function quite happily with several basic apps open.