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.
Even though he did become a king in the end, the epic of Beowulf and his personal character development focuses more on his heroic attributes and his journey or heroism. Throughout most of Beowulf, the author focuses primarily on Beowulf as a hero rather than a king.