In this paper, we analyze and obtain performance of a multilevel Optical Code Division Multiple Access (OCDMA) system with Variable-Weight Optical Orthogonal Codes (VW-OOCs) under the same-bit-energy assumption. The exact error-probability of this system is derived for the Generalized VW-OOCs (codes with arbitrary cross-correlation) which is necessary for the optimum design of multilevel OCDMA systems. We show that the bit power has an important role on determining the performance of codes with different weights. Furthermore, the results reveal that the performance of low-weight codes depends on the weight of the low-weight codes and the code-weight ratio of two classes. Moreover, our exact analytical model has resulted in more accurate performance analysis than the upper bound in [ 12]. We have found that the accuracy of the upper bound decreases when the number of simultaneously transmitting high-weight codes increases.