If you'd like to delete your entire weight history, there are two ways to do this.
Deleting FatWatch from your device and reinstalling it will result in an empty database and all settings will return to their factory defaults.
On the Home screen, tap and hold your finger on the FatWatch icon for a few seconds. The icon will start to wiggle and an "X" will appear on the top left. Tap this "X" to remove the app.
To reinstall, you can either resync with iTunes or download from the App Store. Note that you will not be charged for additional downloads of an app you have already purchased. (This is not the case for music, TV shows, etc.)
You can use Wi-Fi Import to import an empty file to your device, telling it to replace all existing data. This will result in an empty database but preserve all other settings, such as your Goal weight, scale precision, and height.
For more information, refer to Using Wi-Fi Import/Export.
A few people have asked for an easier way to do this. While I agree that the above solutions are a little cumbersome, this is intentional. An operation that is performed infrequently and is very destructive should never be easy to do, as it introduces as risk of it being done accidentally.
In other words, if there were a "Reset" button, somebody somewhere will accidentally push it, and they will be extremely and permanently inconvenienced by the result. In comparison, the inconvenience of using the above methods is minor and temporary.