The small subtitle problem when using AirPlay has been around for a long time and as far as I know, there isn't a fix for it yet. Search the forums here and you will find many people having the same problem.
However, with your setup, you should shouldn't use AirPlay but instead have the AppleTV stream the movie directly from iTunes via Home Sharing. Watching them via Home Sharing will make the subtitles appear properly.
- Configure iTunes and the AppleTV with Home Sharing on the same AppleID account.
- From the main screen on the AppleTV, choose the Computers icon. From here, you will see your shared iTunes computers. Select one then you will see the shared kinds (Music, TV Shows, Movies, Pictures).
Once you locate and start playing your movie, if you don't see the subtitles, click and hold the center select button. This will bring up a screen where you can choose the subtitle language, alternate audio tracks, etc.
If you want to have subtitles on by default so you don't have to manually turn them on every time, you can go into the AppleTV Settings screen and set it to always show them (if available) including which language to show if multiple languages are available.
Hope this helps.