The power has the Weapon keyword, because the weapon you use does factor into one variable of the power: the range. The range is Melee weapon, and without the Weapon keyword, that would become undefined and therefore the power would be unusable from a rules standpoint.
No, it doesn't add the proficiency mod to the attack, notice the lack of Attack: line, and no it does not add it's enhancement bonuses, due to lack of Attack: line, nor randomly rolled damage. It simply allows a specific sort of action which is only modified by one thing.