I have found that the output power that we develop makes a great deal of difference when it comes to the weight carried by the hands. Try this. On level ground shift to a gear that you have to mash as opposed to spinning. As you mash the pedals you can probably lift the hands off the bar. Now shift back to a very low gear where you can hardly keep up with the pedals and notice how much weight is now back on the hands.

If we could pedal a full power in high gears the weight on our hands and our behinds would be minimized while the weight on our feet would be maximized.

I am a very low power cyclist and to get the weight off my hands I need to move the seat forward. A strong rider would benefit more by moving his seat to the rear. This is my observation for myself.

I feel like a perfect bike fit is a moving target as long as the riders fitness level is changing.

Take some seat measurements so if needed you can return the seat to its original position and then start moving the seat around to see if you can find just the right spot for you. Also raise the bars if you can.