In BattleTech, weight class has long been a part of symbology. While it does not match current military symbology, you have to remember that a thousand years have passed and symbology changes.
It does matter in game play, as it helps player quickly recognize the force composition and therefore the threat level. An Assault unit will be slow, yet have high firepower. A light Mech unit is likely to be fast and have limited firepower.
As an informational point, the writer who developed this section is an active duty NCO who is getting ready to retire. He pulled strongly on today's symbology while carrying through the BattleTech symbols that are part of the game.