I think that part of the reason why Soviet power increased in this time period was the strong stranglehold "the evil empire" held on its own citizens and those around it. The control of Easter European nations helped to increase and consolidate the Soviet Union's position in both Europe and its perception around the world. The rise in Soviet power in its belief that it can compete with the West in an arms race helped to strengthen its position in the early stages. Yet, as domestic problems became more apparent and where more repression was needed, cracks began to emerge in the facade. When Reagan came into office, his unprecedented level of military spending, which was enhanced by America's own prosperity of the 1980s, ended up severely hampering efforts for the Soviet Union to continue pace. The increase in research and development of new weaponry ended up creating a situation where the Soviets, under Gorbachev, sought dialogue and discourse as a way of ending the Cold War. Simply put, the neglect of a strong domestic policy for over 30 years and the accelerated rate of military spending had created a situation whereby the Soviet Union's power had to inevitably dissolve.
The growth of Soviet power was directly related to their being one of the victorious nations of World War II. This put them in direct physical control of Eastern Europe for the postwar years. They installed friendly communist governments that were loyal to the Soviet Empire. The "iron curtain" descended on Europe and for the next half century, east Europe remained communist.
As the 1980's came to a close, Soviet economic and military power was already on the wane, and popular pressure grew for reforms. The iron curtain border opened in Hungary first, and within six months, there were popular revolutions across Eastern Europe. There was pressure on Soviet President Mikhail Gorbachev to crackdown on the rebellions, but he refused, essentially letting those countries leave the Soviet sphere.
The power of the Soviet Union grew in Eastern Europe from 1949 on because of the huge amount of power that the Russians had relative to any other country in the Soviet Bloc. The Soviets were able to impose their will on any country in their bloc, as they did, for example, to Czechoslovakia and to Hungary.
The Soviet Union eventually began to lose power as it became more apparent to all concerned that the Soviet economy was not able to give its people all the things that people in the West had. Soviet prestige was also hurt by the Solidarity strike in Poland and by their ill-fated invasion of Afghanistan.
Finally, Gorbachev came to power and pretty much stopped even trying to control Eastern Europe.