Russia once had that economic weight (the world's largest exporter of grain before 1914); they long had the political weight as a member of the Holy Alliance, before Bismark made them a potential enemy, and before the Japanese humiliated them in war; and they possessed a military weight which was overlooked by the Germans to their cost--their invasion of East Prussia in 1914 lead to a disasterous (in terms of the ultimate success of the opening ploy in the west) diversion of troops by the Germans to that front.
That Russia does not possess that "weight" today is a measure of the effect of years of a corruption which the Tsarists could only have envied. They have a very serious potential "weight," and that, coupled with their nukes, gives them a justifiable international power. Brazil suffers many of the same political and social faults which limit Russian today, and they could well become a serious international power, were they to put their national house in order.