I want to move to an apartment that my boyfriend can afford but I can't.
Why does this appeal to you? Do you want to move in together?
I want him to show me he loves me by covering the rent.
I know you want to move to this apartment, but if you can't afford to pay your share of the rent then you probably shouldn't move there. It's not appropriate to make your boyfriend pay so much. The rent should be shared between the two of you.
What about him showing his love by helping me? I can't pay if I move there alone.
Your boyfriend does love you, but you shouldn't expect him to be so extravagant. It is unfair of you to expect this much from him, and if you want to have a loving, respectful relationship, you should be willing to live within your collective means.