All I can recommend is to stick to what is working for you, over the long haul, and let them see your success and NOT see any more massive failures.
Some people just aren’t willing to make the changes in their lives necessary to improve their health. It’s not easy. They are going to have to really want to do it, and that has to come from some change in mindset that comes from within.
Something has to trigger that “snap” where they say - “Enough. I am going to do something about this.” And that is when they are ripe for the information. When they are trying to figure out what the “something” to do is.
Adults don’t like to be told to do things by anyone who they have not already decided is an authority figure. And unless you have a college degree in some specific field, they will never consider their children to be authority figures.
Usually, the more you push / nag, the more resistant they become. So it is better to not start down that path, because then you also have to overcome their desire to not have to admit that you were right about something. Nobody ever likes to be on the wrong end of “I told you so.”
Though that depends on their individual levels of self-awareness and emotional maturity. Some people are very open to advice even if it challenges their existing beliefs. If your parents are like that already, then it would be an easier path.
What I did with one of my sisters who became interested after I had lost about 60 pounds, was to point her to Dr. Jason Fung’s books, and tell her to read them and do some research on her own. She did, and everything he wrote resonated with her and her past experiences with medical care.
She is now well on the way to reversing her type 2 diabetes and is down several sizes in clothing, just after maybe 4 months of low carb plus time-restricted eating.
But the starting point was my own success. That is what gets people to sit up and take notice. I am currently down about 96 pounds from my peak, and have been sticking with it for 9 months (as of today, in fact).
If you have a history of losing weight, failing to maintain it, and going back up, people will use that as “proof” that it is just a fad diet that doesn’t work, and they won’t listen to you.
If you want to change others’ minds, you have to first be an example of what works. Stick to your plan, get healthy, maintain it, and then you will be in a position to lead others.
Also - I suggest not trying to push them AT ALL. If you have been up until now, back off completely. You may have planted a seed in their minds that will grow, but what will fertilize that is your continued success. When they see in 6 months or a year that you have continued to get healthier and are sticking with it, you may notice they start asking a few questions.
That is when the time is right, and you can then point them to the information where they can learn what to do.