Most people do!
To help your hands, try using your non-dominant hand more. Just pick a couple of simple things here and there and try doing them with that hand. Do you know how awkward it is to try to brush your teeth or hair with your off hand? Little things become very difficult but it's helpful.
Not much advice for riding other than just try to build up the weak side more when out of the saddle. Lift some weights, climb stairs, do lunges/squats, and do some extra on the weaker side.