All information entered into Weigh In is stored on your device and is not transmitted anywhere. Of course, if you backup your device to iCloud or iTunes, the data is copied there, but is still available only to you.
No weight data entered into this application is used for analytics, statistics, tracking or any similar activity. It is not visible to anyone outside of this application. It would probably be interesting to see statistics on this kind of information, but there are currently no plans to collect data do this and any change to allow this in the future will require your explicit permission.