What you're trying to do doesn't even make sense.
If there are few equipment methods and those do simple tasks only, you may consider putting them into your Character class.
If there is a complex logic behind the Equipment concept, it's totally acceptable (and favorable) to create a separate class for it.
You can still create a property in your Character class to access the Equipment instance:
Code:
//Equipment class definition omitted
public class Character
{
public Equipment Equipment { get; set; }
public Character()
{
Equipment = new Equipment(this);
}
}
Character c = new Character();
c.Equipment.EquipStuff();
Why do you want to merge them? The fact you are trying to achieve that and that your Equipment class needs a reference to your Character object tell me that Equipment wants to access some data of Character, is that right?
There could be your actual problem. I doubt that equipment needs to know who wears it, so if your's does, your class design is wrong.