Okay. I read all of the posts before our 25 mile ride with two of my solo friends on Saturday morning. All of your suggestions were helpful and we had our best ride yet. In fact, we were pulling into the wind (@ about 22 mph) and held-on at the back with a tail wind (@ 24+ mph). The suggestions regarding relaxation were probably the most effective. Whenever we felt like we were weaving I reminded my stoker (and myself) to relax. I think the net effect of that was to miniimize her micro-balancing and my micro- steering.
We typically spin at between 80-90 rpm and weaving never happened during coasting. Initially, during our first couple of rides, stoker was probably moving around more than neccessary which required more of the micro balancing and steering mentioned above. Also, we both read the article written by one of you for a magizine, the link to which was posted in another thread. Unfortunately I can't find that thread now. Anyway, it was a story about this mtb rider who had some injuries and started tandem riding. He chronicled the evolution of going from newbie to experiecing the "team effect" and then the"tandem team effect". That article was really helpful to both of us.