The people with the best toys often win wars, even if they don't have the best leaders. The US nuked Japan and poof, war over. That does not mean we should spend all our money there though. You only need enough to defeat your strongest enemy, not a bunch of big guns you'll never use.
I think that spending more on your military can maybe buy more weapons and equipment, hire specialists and high-ranking military officials and offer better training. With a strong and well-funded military comes power. If the military is able to take control of a situation due to fantastic training and equipment, they are going to be powerful.
Clearly a country's military spend has a strong relationship to its military effectiveness. The ability to respond to diverse, and often unorthodox challenges, is critical in maintaining a country's lead position in the international system. However, raw military power must be supported by strong economic power and by a healthy democracy. Leading by example, both in the realms of political governance and commerce, is often as important as raw military power.
Yes, spending more on military helps to make a country more powerful, with the caveat that they are in some sort of allegiance with a top 10 military country. Almost all the countries listed in top 10 as having the most powerful military are spending in the top 10 of all countries on their military. Now if there is a very new and upcoming country that is just beginning to increase their military power, spending more would not necessarily make the country more powerful because if a country from the top 10 militaries does not approve, they will suppress that military and the money will be wasted.