Non-orthogonal multiple access (NOMA) has emerged as a significant technique for 5G wireless networks because it increases device connectivity, spectral efficiency, and energy efficiency. The advantages of the NOMA system rely on the employed resource allocation schemes, which include power allocation (PA) and subcarrier user assignment (SUA). Therefore, this paper concentrates on suggesting a PA approach called a weighted energy efficiency power allocation (WEE-PA) approach to maximize the total weighted energy efficiency (WEE) in the NOMA system. Also, the proposed WEE-PA approach boosts the fairness between users, the minimum user rate in the system, the outage probability, and the average data rate per weak user. Therefore, the PA optimization problem defines as an optimization problem with a total power constraint and a set of dynamic PA parameters to maximize the WEE and ensure user fairness. The original optimization problem separates into two sub-problems, and an iterative approach is employed to solve these two sub-problems alternatingly and reduce the computational complexity. Since the optimization problem is non-convex, the sequential quadratic programming (SQP) technique is applied to resolve it and find the corresponding optimal solution. Our simulations confirm that using our proposed WEE-PA algorithm to allocate mutual resources furnishes better results than existing PA schemes.