Legitimate Use of Force & Power Politics

From Max Weber's definition of a state, we gather that the power of a state comes from its monopoly over the use of violence. States guard this use of force jealously and are not inclined to have other actors, especially foreign actors, challenge this right. However, if you look across the international realm, while sovereign states may claim a monopoly over violence, this claim is not equal. It is clear that power politics is at work in just how much of a "monopoly" states can claim over the use of force. 

Countries like the United States and Russia have much more of this authority, it seems, than smaller states like Ukraine or Mexico. Imagine the repercussions if a weaker state like Mexico were to invade Texas, reclaiming territory that it once used to own, and say this action was in response to  the treatment of its citizens at the border and who crossed into the United States? The response by the US, almost undoubtedly with physical force, would be swift and brutal. Much different than what we are seeing with Crimea. 

Even among states that are more equal in international power and standing we see this monopoly over violence differ - at least by acceptance of international actors. Take North Korea and Iran for example. The DKRP, one of the world's most repressive states with a long history of human rights violations, was praised by President Trump as "honorable" and seen as a willing and cooperative partner. Iranian leadership, other the hand, is seen by Trump as maintaining a "corrupt personal terror force and militia" and an arm of its military is even potentially being considered as a "terrorist group". In the eyes of the United States government, the authority and monopoly over violence is more legitimate in the DKRP than it is in Iran.

This authority over the use of violence matters for all nations. The legitimacy and recognition of this right by other actors in the international is extremely influential on what an actor can do both domestically and outside its boundaries. More powerful states can wield this authority seemingly when and where it chooses, whereas weaker states are more constrained in how they can exercise this right. Even domestically a weaker state has to be careful in how it uses its authority over violence.

This leads to some interesting questions:

1. Is the legitimacy of violence really that key of a defining aspect of a state? In other words, is a weaker state with less legitimacy over the use of violence, less sovereign than a powerful state? 
2. Is authority over violence in the international all based on power politics or are there other factors in play? 
3. Do smaller and weaker states actually have an authority over violence in the international or is any authority they do have authorized to them by the major powers?