::: spoiler I was overweight in my late teens and by my mid twenties I was in really bad shape at 340lbs at my worst. I was in a Target with serious chest pains at one point. I'm not a whiner type and have a significantly above average pain threshold, but I wondered if I would even make it back to my car and get home that day. That was in '08. By '09 I had to move back in with family and started riding a bicycle everywhere. I had tried running and rowing when I was younger, and when I was overweight, some of that was from semi regular gym visits and weight lifting. Nothing ever really stuck like a real lifestyle though. They were always things I made myself add to my routine. I tend to overheat from aerobic exercise. Overheating in this context is really hard to define in a relatable way because it is such an intimate concept to my self awareness. Mainly my head tends to get much hotter than the rest of my body in such a way that I am extremely uncomfortable. I can easily put up with that unpleasantness. If I had never gotten into hardcore cycling, I wouldn't have known this unpleasant overheating was even a thing separate from exercise itself.
I come from a background of hot rodding cars. Internally, I always had this notion that I was failing at life if I could paint cars, airbrush graphics, build motors, and fabricate at such a high level, but couldn't do the same with myself and my body as the driver. This curiosity is a major driver in why I rode so persistently through the first couple of months to get past the worst discomfort and made it to a routine. The part that made it different from all aerobic efforts previously was the airflow on a bike, it's massive. The cooling effect got me. I resisted the clothing at first, like everyone does, but after realizing its utility and purpose, it unlocked the cooling effect even more. I made it to under 190 lbs, worked in a bike shop, and raced. It was really the best I had ever felt in my life by a long shot. The lack of impact with cycling also has a fantastic effect on loosening up your body and improving aches and pains. I had felt like I was aging in addition to chest pains and other problems when I was 340lbs but that all went away with riding.
I was super unlucky and was partially disabled by a driver in '14. I had a bunch of broken bones and barely survived. I now walk around slowly, and can't hold posture for very long at all. Still, I can ride. It is nothing like it was in the past. I can only do ~30 miles in a day regularly when I could pull a 100 mile day weekly in the past, and have ridden 200+ miles in a day before. At the present, it does not feel like I can or should be riding, but so long as I maintain my routine that includes nearly daily cycling, I am empirically in my best shape in terms of the least aches, pains, and problems even with severe chronic problems. There is no chance I would be able to establish such a cycling routine from my current state, but I came into my condition as an amateur racer, so I had that advantage and never lost my race legs. If at all possible, consider road cycling. Get a proper bike and get someone to fit you on the bike (adjust and swap required components to fine tune your anatomy to the bike) because with road, the little details are super important or you'll cause issues from that level of repetitive motion. There are a lot of disabled people on bikes too. In a shop, I was the Buyer and often helped people with unique needs. It may not be right for you, but is maybe something to think about. Cycling changes more than your physique, it impacts your physical and mental health in profound ways. Cycling really is a lifestyle. On a bike your both free and anonymous for the most part.
So as car as bike fit and road, if a road bike is fit properly, you won't have weight on your wrists or hands. It probably sounds a little unintuitive, but a proper bike fit on road is all about balancing your weight so that your upper body is neutral without any weight on your arms. Like, the primary test to see if your saddle position is correct is to see if you can pedal smoothly on a trainer while taking your hands off the bars completely.
The key here is that the centerline of the crank arms is the fulcrum of the rider's balance. The adjustment of this balance point is set by sliding the seat fore and aft, thus placing more or less of the rider's posterior to the rear of center.
The only reason I can still ride is because my thoracic (spine section where the ribs are attached) is neutral when I ride, which by inference also means my arms must be neutral too.
I am totally fine with people that don't wish to try it or cycle for whatever reason. I'm simply trying to relate that road bikes are not like any other kind of bike. They are intended to be fine tuned to one's anatomy, and this makes it possible to ride even when many other forms of exercise are not possible. I can't swim or do anything sitting upright, standing, or reaching, yet can ride. GL. I wish you the best.