How long have you been riding? It takes time for your body to adapt to cycling positions, and I find myself feeling a lot of discomfort when I get back on the bike after winter. It takes time for my back to flatten out, and to get comfortable (if you can call it "comfortable") in a low position. But in time I can ride resting my forearms on the tops of the bars, something which I cannot do in my first month back on the bike.
It used to be said that the proper stem length would position the top of the bar so you could not see the front hub when you were in the proper riding position. This assumes that you have the seat in the proper position, as moving the seat fore or aft changes the perspective of the bar.
There is a balance in weight distribution in riding, putting more weight on your hands can reduces the weight carried by your saddle, and vice versa. I like a little more weight on the seat because it allows me to put a little more power to the pedals without having to change my position or stand up. However, my hands still get numb over time if I leave them in same position. The advantage of a drop bar is being able to change positions, and I will move my hands from time to time to prevent discomfort or numbness.