Open the Health app. Tap the Sources icon at the bottom of the screen. Scroll to the WW app and tap on it. You'll see all the available syncing categories both the ones the app can write and the ones it can read. Make sure everything you want is turned on. If you don't see nutritional information as one of the categories WW can write to Health, then it's not an option they have chosen to make available.
WW tends to not play well with others. I don't know what nutritional information the WW app collects but I know they don't allow anyone else to use points.