Call Co-Motion and ask them. They make solo bikes (specifically I am thinking the Americano model) with tandem wheels. I have never ridden a Co-Motion but I rode with a guy a couple years ago that had one. He talked about how solid the bike was.

Thorn Nomad (I have one) is a very robust frame designed for a Rohloff. Some tandems use Rohloffs, so the hub should be able to take your weight. You could call or e-mail Thorn in the UK and ask. If you go this route, they usually use 32 spokes per wheel, I would suggest you insist on 36 on the rear. I built up my Nomad from the frame, I used 36 spoke wheels.

Neither of the above options is cheap, but there are not a lot of robust frame options out there that are less that would not feel like a wet noodle. A custom frame might not be much more and might even be less, you could get one made that takes the wider tandem hub spacing.

If you can cut 500 calories out of your normal diet every day, that is about a pound per week you will lose. A pound per week does not sound like much, but a slow steady approach might give you the best long term solution that is maintainable. Massive attempts to lose weight often fail, a slow steady approach that is not a huge change to your existing diet might be more sustainable. Starting today you should plan on something like this.