You really shouldn't move your saddle to adjust weight distribution. Saddle position affects a lot of things like your knees, hips, and leg muscles. The saddle should be adjusted for those things.

Check the tilt of your saddle though. If your arms/hands are tired and sore, the nose may be too low. Start with making the saddle level (often that takes some thinking because they are curved but the front part where you sit should be flat). Then make minor changes until it's comfortable. If that doesn't help, check your bars and adjust them.