Heavy units are a Class of unit that have the "Heavy" natural ability. Most of those seen thus far are considered the most powerful non-Commander units; presumably, since the only known Heavy 'abilities' are nerfs, the unit receives compensatory buffs that make it extremely useful in situations where their nerfs do not apply. Most heavy units are restricted from entering Tunnels, for example, and can't ride Mounts.
Heavy units may spontaneously pop in Ruins.
Known Heavy Units
Heavy Units may be unable to enter many terrain types besides Tunnels.