Quote: "A game I created using a previous version of AppGameKit has a Media file size of 4 MB that produces an APK file with a size of 10 MB."
Oh you must have used a very old Version of AGK. I had the fun a while ago with the 50mb apk limit in the Play Store and a 3d based game, that had much more media in it.
A hello World APK took about 15mb without any media or code. Well, I stopped development until the maximal apk size in the Play Store increased, but this fact is still sad for small service apps like a compass or a network console.
I don't know exactly where this size comes from.
In Tier2 I can create a whole app in 15mb with 8mb media, but I also heavily reduced the facebook and play store stuff, so I can't tell you exactly what causes this giant size.