Bike comfort

If you haven't already, the first step would be to have your fit checked and adjusted by someone who knows what they're doing (hopefully you have a reputable local bike shop). If your seat is too high, you may be putting a lot of pressure on your wrists.

I would have to agree with Huskyboy that the first thing you should look at is how your hands and arms fit with the rest of your body position. Getting a proper fit is crucial. Changing hand positions while riding is also important. How much do the gloves you wear absorb the shock from the road? Perhaps some wrist-strengthening exercises may be added (I'm not suggesting that you're limp-wristed). Push-ups or curls with the dumbells may strenthen the tendons and cartilage in your wrist.

ALso pay attention to your core strength.  You shouldn't actually be leaning on your arms too much, your abs and back should be doing a part of the work.

Great tips guys. I will go to a local bike shop when I can find the time. Anybody know of any good websites illustrating good bike position?