Yes, this is fair in my view. There are two reasons for this.
First, the UN is set up to try to include all of the nations of the world. This is important so that it can include more countries and allow more countries to make contacts with others. If the UN did not have this system, many smaller countries would not feel that it is in their interests to join the group. They would rightly feel like their voice would not ever be heard in any way and they would simply stay out. This would not help the cause of world peace and understanding.
Second, this seems fair because the UN should be an organization of sovereign states. It is not a world government that represents all the individuals in the world. Instead, it is an organization of governments. Therefore, it makes sense that each government should have an equal say.
If we are willing to tolerate Wyoming having the same number of votes as California in the Senate, we should be able to tolerate the Federated States of Micronesia having as many votes as the US in the UN General Assembly.