Most people will tell you that you don't need an AV program under OS X. If you feel you must use one, ClamXav is free, small, and efficient. It is the most commonly recommended AV for OS X for those that feel they need it.
If Kaspersky has a 113 GB data file... not only is it eating up your drive for some reason, it is also eating a ton of your resources which is likely impacting your performance. 113GB for a data file is huge. I would expect your system is writing to that file almost continuously and what ever process Kaspersky is running is likely hogging some CPU cycles as well.
You should continue to use an AV program for your Windows install under Parallels.
When you say your system was "acting strange"... what were the symptoms?
I uninstalled it last night. No idea why that file got so big, or if it was the cause of my problems of late. There were quite a few:
Hard drive was suddenly filling up. Tech Tool started announcing the start-up disk was getting below 15% and lower, even after I deleted 100GB of files (not the KAV file, other things). After those stopped the system was telling me my drive was full, while the finder showed 100GB+ free space.
External drives wouldn't cleanly dismount (icon would remain dimmed out, system would chide me for disconnect them)
System hangs on restart
I've got two other threads running on these issues.
So far since restarting from SafeMode I haven't gotten any disk full warnings (though it did hang on restart), though now I'm up to 250GB+ free space since deleting the KAV file.