actually just the opposite. avast is supposed to use less memory than most antiviruses. albiet some people with slower computers tend to notice a short lag for a few seconds as the update pops up.
Avast is known as the geek's secret. its what most tech companies use on their computers privatly to keep them safe and then install McAfee or Norton on yours to keep you coming back for repairs. since i had a friend of mine who runs a computer store finally tip me off to it after he felt bad me bringing in my completly shot computer. I have never had issues since.
alot of people recognise it as being the safest form of antivirus out, as it quietly runs in the background constantly, scanning every bit and byte that goes in and goes out the computer for viruses, instead of like McAfee or Norton that do a big scan once a week or every few days that slows your computer way down. it has intrusion alerts, it sets off an alarm when an unauthorized program or person enters your computer without your permission and it picks up on trojans/spyware/adware the second you enter an infected site, neutralizing it and still letting you still browse at your leisure.
it is also one of the few antiviruses that will still run alongside another antivirus (though they suggest you uninstall the others as it will exceedingly slow the computer down) but alot of people with highly protectable material will often run 2 antiviruses and the typical norton and mcafee dont allow this.
as a standalone program it does all the work of Norton, Mcafee and the (horrible) AVG (which takes over crutial DLL's and shares them with their original programs and when it slows down your computer and you remove it, it takes the drivers with them, some people have never been able to boot their computer without reinstalling windows after) but it does Avast does all the work of Mcafee and Nortons expensive antivirus, and their anti spyware and adware and PCcillin (repair) programs....but more importantly it does it while your comletly unaware and quietly in your backhround so it never interupts your computer pleasure. (you can still look at the reports if you want to watch what its doing)
So my only thought as to why your computer may be slower is either the original antivirus was never uninstalled properly, a virus repair or adware/spyware software was installed as well or someone downloaded a program or game from online and approved it, letting it in. plus unsafe DL programs like Limewire or Napster that are allowed into your computer can let viruses in past the Avast security because you have approved the program itself (should regularly do a forced scan of the shared folders after downloads to double check for viruses)
but i have personally never experienced any ram loss, loss of space or lag from Avast, nor have any of my family or friends