Looking for small, light Android phone with GPS and Barometer

[billdz]

Hi,
To use an app that would enable me to use a phone as an airplane/drone/model rocket tracker, I need a phone that has all of the following:
* small and light
* Android 4.1 or higher
* GPS
* barometer
* unlocked

I used the Phone Finder at http://www.gsmarena.com/search.php3? but could not find anything lighter than a Nexus 4. This phone would be great, it weighs just 52 grams, but it lacks a barometer:
http://www.poshmobile.com/catalogue/micro-x-s240/

Not sure if the Phone Finder is comprehensive, so I'd like to ask if anyone knows of any better candidates. Best options found through Phone Finder are the Nexus 4, Moto X, and Galaxy S4. Guess these days everyone wants a bigger phone.

Thanks,
Bill