OK, science folks...

I enjoy riding my bicycle with an infant seat for my son on the back.  I weigh about 200 pounds, my son is about 30 pounds, and the bike with seat is around 40 pounds.  There are several hills in the area around my home, and while climbing one, a thought struck me.  My body connects to the bike at about four places, one foot on each pedal and one hand on each side of the handle-bar.  I was in a very high gear up a steep hill, but my legs were still tiring.  What I'd like to figure out how to calculate is how much force I was demanding from my thighs with each pedal?  It much be less than my body weight, as my downgoing foot stayed attached to the pedal, weight was still transferred from my hands to the top of the handlebars.  I have regular pedals, not click-in shoes, so the up-going foot is as light as possible.  Any ideas how to work the kinematics to figure it? 

If I maintain a constant speed going uphill, then the force out of my thighs should be the same as the portion of the weight vector parallel to the slope of the hill plus friction losses?

Thanks for any ideas!

-Cheese