www.makemkv.com

I use makemkv when handbrake has problems backing up my DVDs. But when I use makemkv the mkv file is nearly the size as the DVD. A double layered DVD backup can reach the size of 8GB+. I can then take that file and use handbrake to shrink it down. But is there anywhere in the settings of makemkv where I can adjust the size of the file it creates?

Not really, because what you get is a copy of what is on the disk. Making it smaller (or larger) involves recoding what is there... and that's what handbrake does.

It gets worse with Bluray, of course... a 48 minute Doctor Who episode is 8-12GB on BD, under 2GB on DVD.