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.
The Epic Hero. Understanding the significance of Beowulf's acts requires an understanding of the key figures in the epic poem. A hero of the Geats in Sweden, Beowulf renders aid to the King of the Danes, Hrothgar. Hrothgar's mead hall has been attacked by Grendel, a powerful monster, and his mother. Beowulf heroically slays Grendel and becomes the target of his mother.