Let the weights of Abby, Bart, Cindy, and Damon be $ a $, $ b $, $ c $, and $ d $, respectively. We have the equations \begin{align*} a+b&=160\\ b+c&=180\\ c+d&=200 \end{align*} Subtracting the second equation from the first, we have $ (a+b)-(b+c)=160-180 \Rightarrow a-c=-20 $. Adding this last equation to the third given equation, we have $ (a-c)+(c+d)=-20+200 \Rightarrow a+d=180 $. Thus, Abby and Damon together weigh $ \boxed{180} $ pounds.