The article that Jerry posted is good. The other thing that's easy to do when you first start riding with "stuff" is to use to big of a gear and mash. Dropping a gear or two and spinning easier will be easier on your knees as well.
I agree. It's similar to the strange inclination to mash the pedals into the wind. I suppose we get used to seeing the ground move beneath us at a certain speed when we are in a certain gear range and unconsciously try to reach the normal state by pushing that gear a bit harder. Maybe use the granny if you don't normally.