Avast 4.6.691, Home edition, sensitivity set high, on Win2k Pro;
ashWebSv.exe uses 13,234,176 Bytes (12.62 MB).
Avast does not have a noticeable slowing down effect on this 1.6 GHz computer.
If the memory usage keeps growing there most likely is a program running written in some C language that does not have a proper memory management.