In this paper, a novel non-uniform Binary Concentration Shift Keying (BCSK) modulation in the course of molecular communication is introduced. We consider the nutrient limiting as the main reason for avoiding the nanotransmitters to release huge number of molecules at once. The solution of this problem is in the utilization of the BCSK modulation. In this scheme, nanotransmitter releases the information molecules non-uniformly during the time slot. The 3-dimensional diffusion channel with 3-dimensional drift is considered in this paper. To boost the bit error rate (BER) performance, we consider a relay-assisted molecular communication via diffusion. Our computations demonstrate how the pulse shape of BCSK modulation affects the BER, and we also derive the energy consumption of non-uniform BCSK in the closed-form expression. We study the parameters that can affect the BER performance, in particular the distance between the nanotransmitter and the nanoreceiver, the drift velocity of the medium, and the symbol duration. Furthermore, we propose an optimization problem that is designed to find the optimal symbol duration value that maximizes the number of successful received bits. The proposed algorithm to solve the optimization problem is based on the bisection method. The analytical results show that non-uniform BCSK modulation outperforms uniform BCSK modulation in BER performance, when the aggregate energy is fixed.