Non-orthogonal cyclic prefixed filter bank multiple access (CP-FBMA) is a newly proposed waveform with many attractive features. An important aspect is that the design freedom of the filters is released due to removal of the orthogonality constraint, which is exploited in this work to maximize the average weighted sum rate (WSR) based on statistical channel state information (CSI). Since the average rate has no closed-form expression, we asymptotically approximate it to simplify the problem. With the asymptotic rate, a full-band waveform optimization algorithm is proposed, which is based on manifold gradient ascent. Moreover, stop-band energy constraints are added to represent the requirements on the spectrum occupation, and an algorithm combining successive convex approximation (SCA) with consensus alternating direction method of multipliers (ADMM) is proposed to cope with the modified problem. Numerical results show that the asymptotic rate can approach the average WSR obtained by Monte-Carlo simulations. Besides, the average rate of CP-FBMA can indeed be enlarged through the proposed algorithms.