In total, the file size of the SDK will depend on what features you implement in your app. Using an optimization method called App Thinning | Apple, the SDK will add ~400KBs to the downloadable binary.
When you include the Airship SDK in and build your app, the compiler will take only the relevant files from the SDK needed for Airship functionality.
This means, if you are not using a certain feature, such as the Message Center, it will not be included in the app when built. For detailed information on "Best Practices", please see our mobile documentation. Our recommendation is to build your app and then look at how including the Airship SDK will change your specific app's download size.
Thus, the larger answer is the size of the Airship SDK will vary.