Whew. What's in this relationship - love? On his part? Is he helping your efforts to lose weight, when you make the effort, or does he make it more difficult? There's more to your relationship than just arguments about your weight (criticism), but no need to analyze that here (a helpful therapist would offer some insights). What is important is for you to realize that nothing changes unless you are in a position to make changes. If he's 'completely willing to give up the relationship,' then that's your handwritten invitation to leave the relationship yourself. When you are ready, you'll do that.
Fitday can help you in your efforts to lose weight and stay healthy. You can do that with or without him, Fitday doesn't care. It's just a tool, but an excellent tool!