A constitution is a statement of the basic principles and laws of a nation, state, or group, such as the U.S. Constitution. Another very common meaning of constitution is the physical makeup of a person. So think of a constitution as how a body (yours, the government's) is set up. If you have a strong constitution, it means you don't get sick very often.
I think the focus of the story is on Beowulf as a hero rather than a king because it is his heroic deeds that lead to him being offered the throne. Also to be king one must possess some type of heroic qualities in order to rule a land and its people.
Sir Gawain versus Beowulf. A true hero is one who is willing to sacrifice his own existence for the life of another. Two characters portrayed as heroes are Sir Gawain, a character from the tale Sir Gawain and the Green Knight, and Beowulf, another character from an ancient British epic entitled of the same name. The difference between Beowulf and Sir Gawain, is that Sir Gawain is a real hero, and Beowulf just thinks he is.