Your boyfriend sounds like he has a severe fetish. I don't say that to kink-shame. Having non-conforming sexual preferences are fine, but this fetish is to the detriment of your health and well-being. That's not fine.
We're the same-ish height and roughly the same age. I turned 30 the year--morbidly obese with an unhealthy relationship with food and all the stuff that comes with that: health issues/acne/etc. Then I decided to do something about it. My husband (also a big guy) did not exactly make it easy in the beginning, so we had a sit-down, heart-to-heart discussion about how I needed him to be supportive of my journey. I didn't expect him to start going to the gym right beside me, but I did expect him to stop buying me pizza and junk food on the regular.
I wish I had made the decision to focus on better myself sooner, and I wish we had had that talk sooner because I'd be alot further in my weight loss journey... but I can't change the past! I can only change the future, and that starts with today's decisions to eat right and get off my butt.
If your boyfriend can't respect what you *need* to do to better yourself, then it's natural that you're contemplating ending the relationship and ultimately finding someone who will respect you and love you regardless of your size.