Heterogeneous networks (HetNets) technology is expected to be applied in next generation cellular networks to boost system capacity. However, applying HetNets introduces a significant amount of interference among different tiers within the same cell. In this paper, we propose a weighted rank constrained rank minimization (WRCRM) based interference alignment (IA) approach for three-tier HetNets. The concept of RCRM is applied in a different way to deal with the basic characteristic of different tiers: their different interference tolerance. In the proposed WRCRM approach, interference components at different tiers are weighted with different weighting factors (WFs) to reflect their vulnerability to interference. First, we derive an inner and a loose outer bound on the achievable degrees of freedom (DoF) for the three-tier system that is modeled as a three-user mutually interfering broadcast channel (MIBC). Then, the derived bounds along with the well-known IA feasibility conditions are used to show the effectiveness of the proposed WRCRM approach. Results show that there exist WF values that maximize the achievable interference-free dimensions. Moreover, adjusting the required number of DoF according to the derived bounds improves the performance of the WRCRM approach.