Weitzman implicitly shares my concern with climate models. Obviously, we have nothing to worry about if the models are too pessimistic. If it turns out that over the next decade global temperatures edge down, or rise more slowly than the models predict, then we will be relieved.
The troublesome possibility is that the models are not pessimistic enough. In fact, Weitzman would argue, and I concur, that the case for doing something today about global warming rests on the fear of the scenario of accelerated near-term climate change -- increases in temperature at a rate that is on the high end of the range being forecast by climate models.
The ideal approach would be a "just-in-case" climate-change mitigation plan. If global warming stays at or under current baseline projections, we probably would do best to simply just adapt. However, if global warming accelerates, we would want to take strong steps to counteract it.