I had this same problem and just discovered a solution!
Problem: My Weight Watchers app stopped syncing with my Apple Health app to track my steps (it had previously tracked my activity). I tried tapping the "sync" option at the bottom of the activity page, as well as refreshing the page by pulling down the page, on the WW app as previously suggested and it did not sync.
Solution: I discovered that my Apple Health app had disconnected from the WW app. To reconnect I opened the Apple Health app, selected the "Sources" option at the bottom of the app (the little heart with an arrow). I selected the WW Mobile option and discovered that the categories had all been turned off. To fix this, I simply selected "Turn all categories on". I then shut down the Apple Health app (double click the home button and slide the app up on the screen) as well as the WW app (close the same way). When I reopened my WW app, my Apple Health activity had synced and now seems to be working properly.
Good luck and happy tracking!