I'm going to take your word for it that her weight is not an issue to you in terms of you finding her attractive. Good.

Just being "morbidly obese" by BMI is not an early death sentence. A lot of healthy people fall into the obese range, and also, a lot of relatively fit people suffer the same health problems that obesity is supposed to lead to. I'm not saying that your GF's weight doesn't put her more at risk of those problems than a person who eats right, but if she stays the same size she's at, it's not a definite that they would happen anytime soon just because she's obese. Or a definite that they wouldn't if she got smaller. So I'm not sure that this is an emergency that needs to be addressed early in your relationship.

That being said, she's young but her weight probably will have some effect on her life down the line, whether it's not being able to do active things with you or limiting your sex life or potentially her mobility. For me, as a person who's classed as "severely morbidly obese" also, the decision to lose weight didn't happen when I was faced with the idea of diabetes or heart attacks because my medical tests have always been healthy. It was those day to day issues that had the biggest effect on me and that got me started.

You're in love. Your GF has a person who supports her no matter what now. That is a powerful thing. There is a lot of guilt and shame tied up into being obese for a lot of people, especially women, and I think the best thing you can do to help her live a healthy life is love her. Help reinforce that she's a worthy person, despite all of the hurtful messages she gets out in the world. Model a healthy lifestyle for her not as some kind of regimen she needs to get into so she doesn't die young, but as fun things that you can do together and feel great after doing.