I answered your question a little while ago: Does the notion of 'heavy' infantry and cavalry actually exist in ancient texts? The name refers to the weight of the equipment. The classification is at least as old as the 5th century BC, although the first to be named by a weight adjective was the light infantry, not the heavy.

There is another relevant reply from /u/dandan_noodles in that thread, to fill you in on the Napoleonic period when these designations are very widely used.