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.
Beowulf is the hero and title character of an Anglo-Saxon epic poem. The poem was written in England, though the action is set in Scandinavia. It takes place in the 5th and 6th centuries CE, but was written some time between the 8th and 11th centuries. Beowulf is among the most important extant Anglo-Saxon works of literature. According to the poem, Beowulf was the son of a Swede, EcgÃeow, but grew up among the Geats. EcgÃeow had been banished before his son's birth because he was unable to pay a high weregild, a type of fine imposed on those who had killed a man.