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.
left for home, and Beowulf held the gift seat, ruled over the Geats. He was a good king. He avenged Heardred's death in later days, became to the wretched Eadgils a friend, supported that son of Ohthere over the wide sea with men and weapons. On a cold expedition he deprived king Onela of life. Thus had that son of Ecgtheow survived each battle, terrible war, much courage-work, until the day when he fought the dragon. Beowulf Visits the Dragon. Twelve enraged men paid the dragon a visit. The king had by then learned how the feud arose, this affliction of men: to his possession had come, through the hand of an informer,