From the question, we have some equations:

\(\left \{ \begin{array}{l} A+B=150\times 2=300\quad(1)\\ B+C=127\times 2=254\quad (2)\\ C+D=168\times 2 =336\quad(3) \end{array}\right.\)

We do the following operation \((1)+(3)-(2)\). after that, we have \(A+D=300+336-254=382\).

Therefore, the average weight of sheep A and sheep D is: \(382\div 2= 191\)(pounds)

Note that \(A,B,C,D\) is the weight of each sheep A, B, C, D, respectively.