Variable-weight optical orthogonal code (OOC) was introduced by G-C Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirement. In this paper, a construction for optimal (υ, {3,4}, 1, {s/(s+1), 1/(s+1)})-OOCs is given. For s=2, it is proved that for each prime υ≡ 1(mod 24), there exists a (υ, {3,4}, 1, {2/3, 1/3})-OOC. A recursive construction for cyclic difference family is also presented. By using these constructions, a number of new infinite classes of optimal (υ, {3,4}, 1, Q)-OOCs for Q = {1/2, 1/2} and {2/3, 1/3} are constructed.