The Apk file exported from Android Studio is too large

The difference is due to the appcompat library which is compiled in by default to New Project Wizard-generated projects in Android Studio if you target an API level lower than 14. When I ran a test, the size increase was 642k for a debug APK, and 411k for a release APK (with Proguard enabled -- that will strip out unused code but not unused resources).

There's not a lot you can really do about this, short of removing the appcompat library if you're not using any of its features (though you should probably be using its features).