Could be your saddle is too narrow. My bike's stock saddle was too narrow at the sit bones so I couldn't really put enough of my weight on them. The result was more weight on the pubic bones. A wider saddle may support your sit bones better.

Or, try tilting the nose DOWN. Play with it and stop before you feel like you're having to hold yourself up with your hands. This works the best for me while maintaining a more aggressive position with the bars. Right now, my saddle is set pretty straight, but in the spring when I do criterium racing, I will lower the nose to make it more comfortable to spend a long time in the drops.