Double-weight optical code division multiple access (OCDMA) systems are proposed for studying differentiated quality-of-service transmission. Based on quadratic congruence code (QCC), we construct a one-dimensional double-weight code family, which can be well utilized in incoherent synchronous double-weight OCDMA networks. By introducing algebraic transformation to code sequences of QCC in level 1, we obtain multiple double-weight codes with cross-correlation 1. Under the same-bit-power assumption, the performance of low-weight codes can be significantly improved and is always superior to that of high-weight codes in double-weight OCDMA systems with power control. This property is contrary to previous conclusions under the same-chip-power assumption.