this is just some speculation from a 2bad46s HL lobby player but I thought it was an interesting question, correct me if it doesn't make sense

Generally in 6s there's two enemy Scouts and no friendly Pyro to airblast an Uber away if you get caught in a bad position. So when the enemy gamers have Uber advantage Heavy can't put himself in a useful place to do damage or he'll be ripped to shreds as soon as they push.
Against the classes in a 6s setup Heavy is good at defending the Medic from bombs but that leaves a sensible roamer either alive and on the flank more or offclassing to Sniper while the rest of the team can simply +backward when they hear his gun spinning up. In HL Heavy can be extremely strong in a push by cornering and engaging the enemy Heavy as his DPS:health is unmatched. The winner of these situations often results in more than one kill as enemy players are playing around the Heavy for protection.
There is not a situation like this this in 6s as the enemy gamers can mostly run or jump away before being cornered. If they are caught out Heavy's Minigun is not especially strong compared to the Demo, Scout, or Soldier weapons due to the delay from spin up and its eventual maximum damage is purely overkill for anything besides the buffed and healed enemy pocket as the enemy classes have comparatively little HP.
Heavy's other advantage, his 450HP maximum health, could be detrimental to his teammates as he can't dodge and avoid damage. Full overheal buffs last the same amount of time (15 seconds) for all classes but healing is a set amount of health per second. There's less useful unlocks, no Sandvich to save the Medic, no Fists of Steel to escape, no GRU (or fast whip soldier thing) to get to mid at a reasonable time.

TL;DR: he can't escape from bad positions or get to useful positions fast enough, he's no more useful against a single enemy than the other classes, and it takes more time for a team to be healed to its maximum potential.