norwood

Actually the opposite is true. Moving back will generally take weight off the hands and wrists. Unless there's some other unknown factors in this case. The OP's hand aren't slipping, the butt is sliding forward on the saddle. That said, I agree, a bike fitting may be needed.
That saddle looks uncomfortable, but saddle comfort is entirely an individual issue. If you can't tilt the nose up a bit without discomfort then maybe a new saddle is in order. If you end up with a Brooks, you will likely need it tilted up in front as they can be slippery at first.
All this begs the question, does the hybrid fit you? I.E. is it the right size? One of the problems of riding a bike that's too small is your weight ends up nearly centered over top of the BB and the "remedy" is often sliding the saddle back to the extreme and/or a long stem length to keep from being scrunched up which results in the hands and wrist supporting most of the upper body weight.