Alright, a few things. First, there is nothing wrong at all with the frequency that you're having sex. The majority of those in long term relationships at your boyfriend's age have sex less than that. For those couples around about once a week is decent enough, though that's often with children which obviously makes sex more difficult. But that aside, there is no issue with the frequency. Obviously you have a higher sex drive than him, which is fine and something you can talk about. But it doesn't mean that there's anything wrong with him. From a sex drive perspective, there doesn't seem to be.
If you want him to have sex more, I think the obvious thing to do is to fall in line with his routine. You say when you get into bed he's fast asleep turned the other way. Well, yeah. What do you expect? He is fast asleep, and needs to be up in a few hours. As much as being woken up for sex can be a thrill, it needs to be at the right time, and the middle of the night when you need sleep in order to get up to work is not the right time. You say that you don't like sleeping in the same bed as other people, but that is legitimately a pretty awkward thing to do when you're going to bed several hours after him. This would all be so much better if you went to bed and got up when he did, or perhaps stayed in bed for an hour or so if you want a bit more sleep. It would give you a better routine, it would allow you to interact more with him, and for my money it would make it significantly more likely that he'd be up for sex when you go to bed at the same time. I would also hope that it would help you with your anxiety around sleeping together in the same bed if you go to bed together, either have sex or at least spend time talking, cuddling, reading etc, and then go to sleep together.
You obviously need to address your lifestyle and lose weight. You know that. But routine, particularly going to bed and getting up at the same time every day, has a huge impact on that alone. I also expect it will have a good impact on your relationship in terms of sex and other things too, so that is the obvious first thing I would try to do.