In the greater scheme of things (after all it is a security application) memory is there to be used, especially if on windows default settings performance is king, so memory will be used where possible/available to help with performance.
Looking at the task manager on my XP Pro system, avast doesn't use much on my system and compared to others is frugal. Just look at another security application example, MBAM, not only is the mbamservice.exe much higher than avastsvc.exe, it also has two other services mbamscheduler and mbamgiu which add another 12mb to the RAM use.
Not only that mbam is also a bit of a CPU hog at times, as seen in this screenshot and all I was doing was browsing/compiling this and capturing the screenshot.
There are many other application that aren't security related and these can be RAM hogs, well in excess of avasts resource use.
Some time ago the avastUI was using more memory than it is now on 9.0.2011, now I don't know if that is/was a memory leak, if so it would appear something has been done in regard of the avastui.exe memory use.