I recommend getting a pro bike fit. There's a lot you can do on your own, if you want to read up a lot on bike fitting. But a good fitter will get you there a lot faster. Though even then, they're not perfect.
I agree that your bars are rotated back and your levers up much more than normal. It's very unlikely that this sort of extreme setup is appropriate.
I've struggled at times with excessive weight on my hands and some hand numbness as a result. This got much better when I lost some weight. Short of a very upright and non-road bike setup, being overweight is going to result in more weight on your hands. It's just physics. Also, the more effort you put into pedaling, the more you'll take weight off your hands.
In my case, I tend to a slightly nose up saddle (somewhat unusual), but this helps support my pelvis and helps me hold weight off my hands. I don't get any discomfort in the saddle area as a result. So, this works for me.
While counter intuitive, it's not uncommon to get more comfort the more you drop the front end. Up to a point, of course. So, don't assume more upright is inherently going to be more comfortable.
Even with a perfect fit, body parts can hurt if related areas are not strong enough to support them properly. So, some off-the-bike exercises may be called for. Especially strengthening your core.