Synchronization, export and restoration are different capabilities. Do not assume that one implies another.
What is documented for Weights
The released listing confirms iPhone and iPad support plus a ZIP export with PDF and CSV files. It does not verify automatic iCloud synchronization or import of an exported archive.
Before changing devices
Keep the old device and inspect an export before depending on a transfer. Check that the records you need are accessible on the new device before removing the old copy.
Ask a precise support question
Identify your app version, old and new devices, and whether you need a readable export or an in-app restoration. Do not send private records unless needed and deliberately chosen.
Export, sync and backup are different tasks
An export creates a file you can inspect outside the app. Synchronization keeps records aligned between supported endpoints. A restorable backup needs a documented route back into the application. One does not establish the others. Weights documents a ZIP containing PDF and CSV output; that description alone does not confirm automatic iCloud synchronization, an import screen or recovery after deleting the app. Check the precise workflow before making a device change.
A cautious device-change checklist
Keep the old device and its app data while checking the new one. If export is available, save the archive somewhere you control, open it and inspect a recent record and an older one. Confirm what the files contain rather than assuming an archive is complete because it downloaded. Ask support about transfer or restoration if those steps are not documented. Do not delete the only known copy while a transfer remains unverified.