The thing is, other than that, our relationship is pretty much perfect.

Always love seeing this rationalization invoked. Think about it: the state of your relationship's sexual health is not good, and that's a huge part of any serious relationship. It's huge. So you saying the relationship is perfect, other than this huge issue which you've said is "consum[ing] [your] relationship", is akin to saying "Yeah, my day was great except for the part where my hand got chopped off." But I'll never stop seeing this rationalization on /r/relationships threads. I know.

Now, to your issue: honestly, it's okay that the intensity of your sexual attraction to someone is partially based on that person's weight. That's natural. The problem is in your priorities:

I often tried to disguise it as a concern for her health (which was not a lie, this was an honest concern)

But let's be honest though, her weight is primarily an issue for you because of the waning sexual attraction. The post overall strongly suggests that. So now I'm forced to ask: what motivation and encourage have you provided? What strategies has she pursued for losing weight? Because I know for a fact that it's harder to lose weight if it's largely to please someone else; you're not attracted to her while she's overweight, and if she's actively conscious of that perception, it will make it that much more of a struggle for her to lose weight. She has to believe in herself. So what have you done to motivate her? Because, strangely, there's nothing in your post about that. You're her partner: what kind of environment are you providing for your partner who is trying to lose weight?