Welcome to Psych Central, dytikos.

I've been following what you & medievalbushman have written. (And, by the way, I think medievalbushman has done a remarkable job of replying to your posts. So I won't try to go back over territory that the two of you have thoroughly covered already.)
What I want to focus on is your relationship with your girlfriend. Just by way of reference I'll mention that I'm an old man & my wife & I have been married for almost 40 years. But at the same time, I've also waged a life-long struggle with my gender identity. It's a long story & I won't bore you with all of the details. But I managed to keep my gender identity issues (plus some other stuff I won't go into) a closely guarded secret for my entire life up until about a dozen years ago or so when my gender issues finally came awkwardly spilling out. And, since then, although my wife has been willing to accept what she has learned about me & move on, she really wants nothing to do with it. So we have sort-of a don't ask / don't tell policy going on here. I did see a therapist for a short time following my unfortunate disclosure. And while I was doing so it was so refreshing to have the chance to talk about things I had kept hidden literally for decades.
What I want to suggest to you, with regard to your relationship, is that this fetish situation (if that in fact is what it is) is something that may be with you in one way or another for a lifetime. These sorts of things can be like whack-a-mole. You stuff it down one way & the next thing you know it pops up again someplace else. So the question here, I think, is... is your love for your girlfriend, & her love for you, strong enough for the two of you to weather this together. This is not just your problem... or your gf's problem. It's both your problems. And, as medievalbushman has pointed out, you each own various aspects of it.
If it would come to pass the two of you do grow to adulthood & marry, your "fetish" (if in fact that is what it is) is just one of many hurtles the two of you are going to face throughout life. Having been married for almost 40 years now, I think I can say with some authority it takes an ocean liner's worth of compassion, forgiveness, understanding, & yes just downright stubbornness to keep a romantic relationship going for that length of time. So if your gf is ready to throw in the towel, so to speak, already over this one thing that does not, to my mind, bode well for your relationship, sad to say. But if the two of you can come together & own the problems you share together, then there is much in your relationship to be hopeful about.
I know you mentioned you can't see a sex therapist. But I'm not sure a sex therapist is what is really called for here at this point anyway. To my mind, perhaps what is needed is something more along the lines of a couples counselor (or therapist)… someone who can work with the two of you to learn how to handle your mutual problem (your "fetish" as well as your gf's weight-related concerns.) This is not simply YOUR problem, or your gf's problem. It's a relationship problem the two of you share & need to learn to resolve. The question is, really, do you love one another enough to do what you need to do to stay together. Only you & your girlfriend know the answer to that question.
Here are links to 4 articles, from Psych Central's archives, on the subject of communication within relationships as well as on the secrets of happy couples:
9 Steps to Better Communication Today
oth.
5 Secrets to a Successful Long-Term Relationship or Marriage
The 10 Secrets of Happy Couples
The Secrets of Great Relationships
My best wishes to you both.