The problem with this seems to be with the way the game tracks completion of the resolution.
The lose weight and get fit resolutions seem to use a custom method for tracking the fitness or fatness changes - " event_testing.custom_tracker_objective" - which seems to have broken after one of the game updates.
If they fix that, or switch to some other tracking method, then the resolutions should start working normally again.
For console players, I don't know of any workaround, other than avoiding these resolutions because they can't complete.
For PC/Mac players who are ok with using mods, but aren't aware of any that can help, @Logicalli/Rifsunot has had one out for a while that is linked to from the Hero approved Common Game Fixing Mods thread. It's a script mod that fixes the custom tracking Python code. I also have a mod for it on my site, which is a non-script mod that works by switching the tracking method for the resolutions over to the same one that other (working) resolutions and objectives use.
Hopefully, it can be fixed someday, since it doesn't seem to be a complex issue and we've pointed out what the cause seems to be - but if you've experienced this bug, click the Me Too button on the first page of the thread.