A configuration with \(v\) treatments and \(b\) blocks, each of size \(k\), is called a balanced incomplete block (BIB) design if every treatment appears in exactly \(r\) blocks and every two-element subset of treatments occurs in \(\lambda\) blocks. Furthermore, if the \(b\) blocks can be partitioned into \(t\) sets of \(m\) blocks each in a way that each treatment appears exactly \(\mu\) times in each of the \(t\) sets, then the BIB design is said to be \(\mu\)-resolvable. Moreover, a \(\mu\)-resolvable BIB design is called affine \(\mu\)-resolvable (\(\mu\)-ARBIB) design if any two blocks belonging to the same set (different sets) contain \(q_1\) (\(q_2\), respectively) elements in common. For \(\mu= 1\), the \(1\)-ARBIB design is simply called an (affine) resolvable design. The authors present the construction of some optimum chemical balance weighing designs by using the same results characterizing the \(\mu\)-ARBIB designs.