Is there a way to back up Amazon Market via Titanium Backup without 2Gb backup file size?
Amazon app store downloads APK files to a folder that Titanium Backup considers external app data. You can regularly clean out this folder or choose one of the following:


Create a label, and add Amazon Appstore to it. Now go into settings and under Backup external app data choose.
"Enable for apps outside of choosen label" now pick the label that you added Amazon too. 
Inside TB's settings under Backup external app data choose "Enable if it's smaller than choosen size" and enter a value that you're comfortable with.