Kathi- I think what you perceive as lack of upper body strength is actually lack of core strength. If you're putting too much weight on your handlebars your core isn't holding you upright.

Upper body strength comes from the core. think of your arms as springs and your core as either a marshmallow or a rock.
If you push a spring against a marshmallow to launch it, it won't go very far but if you push a spring against a rock to launch it - ZOOM!
Become a rock