In the early US in order to qualify to vote one was required to own land(as well as be white). The precept being that only those people who owned land had a real investment in country and thus deserved to have a say in how the country was governed. This was a very simple merit test and certainly not one that was scaled upon merit. It was a simply yes you are white enough, yes you own land, and yes you have a penis(though I have found no proof that this was actually verified). The US has always been guided by a principle of one man one vote, again provided you deserved your right to vote...
According to Wikipedia China may have first dabbled with a meritocratic government around 165BCE. The system allowed any that could pass certian knowledge tests to get a position in the government.
The system allowed anyone who passed an examination to become a
government officer, a position which would bring wealth and honour to
the whole family. The Chinese Imperial examination system seemed to
start in 165 BCE, when certain candidates for public office were
called to the Chinese capital for examination of their moral
excellence by the emperor. Over the following centuries the system
grew until, finally, almost anyone who wished to become an official
had to prove his worth by passing written government examinations.
As for what a system like you suggest would be called...
I can only see 2 potential paths. The first is Oligarchy. Since having more money would result in more votes, the very rich would effectively hold all of the power. Even if it started out on an even playing field gaining more wealth results in more power inevitable those who crave power would horde the money and in a relatively short amount of time the very few are in charge. This system creates a benefit to creating a permanent underclass which has virtually no power, and is ripe for exploitation and corruption.
If the system were somehow balanced to prevent any relatively small group of people from gaining excessive power, and prevents the hording of power, you would have a system that promotes Social Darwinism. These sorts of rewarding effectiveness systems are what some say allowed the US to become a power house in the 1900s. It is also associated with the Nazi's.