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.
[preview] Beowulf as an Epic Hero - What are the qualities of an epic hero. An Epic hero is a hero on a quest, with superhuman powers displaying courage, generosity, and loyalty. Translated by Burton Raffel, the epic story Beowulf is one of the best and well known epics of its time.