Weight Loss Tracker & BMI is a simple, focused app. What it does is described here in plain words.
Everything you enter is stored on your own device. There is no account to create, nothing to log into, and no analytics or tracking SDK in the app. Syncing with Apple Health and with your own iCloud is optional and off until you turn it on. The privacy policy sets out exactly what that means, including the one third-party service involved when you buy a subscription.