While riding consciously engage your core and attempt to hold your body up. Keep wrists straight. Ergon grips (adjusted properly) help with this. You may also find tipping the saddle nose up a tiny bit helps. It'll take some weight off your hands.

It seems contrary, but I've found that overly padded gloves and/or grips can make things worse. The tendency when using them is to grip harder to get a secure feel, which limits blood flow.