I had the same thing.
In the end I swapped out by 100mm stem for a 120mm stem and this has really helped the issue.
The shorter stem meant my heavier, than my arms, torso was further forwards relative to my arms, which put more weight on my hands. The longer stem means my torso is further back relative to my arms therefore taking some of the weight off...
Moving the seat back should have the same effect as it will increase your reach, but don't compromise your riding position relative to the pedals as that can affect your legs, give you cramps etc...