Halo has some excellent advice / feedback here.
One thing I would add is that you can spin up while in the air without losing forward momentum
during spinup. So when you are running forward and you know you want to fire, jump a split second before starting spin-up. I'll often do this when going around corners and land from the jump just as boolets are beginning to fly from the minigun. You give folks a little less time to hear the spin up and you land in their lap pretty often, and when you are firing into someone's face with a minigun, they generally find themselves in spawn a few seconds later. The exception to this is when you know there's a SG around the corner - jump into a SG and you will be pinned to a wall while the uber your medic popped runs out... i cri ever tim.
With heavy it is all about getting in close so you can dump the maximum amount of hate out of your weapon. Knowing the map and the choke points is key. On turbine, for example, the heavy tends to rule the vents because it is so easy to keep folks in max damage range. Running across mid, on the other hand, stinks - Remy/Rose/Mini/Lockhart/36/freshmeat/Mobilize will ruin your good time in a heartbeat with a well-placed headshot on your ginormous waddling body.
Getting across open spaces is tricky. I used to use the Gloves of Running Urgently and still do occasionally because they help you close the distance so quickly. Those mini crits you open yourself up to while wearing them must be managed properly though. Pick your route carefully - use cover as often as possible to break up the sight lines of snipers (crates in mid on turbine are good for this and the stairs to an extent).
I'm now using The Fists of Steel because you can absorb a 100% headshot from Remy/Rose/Mini/Lockhart/36/freshmeat/Mobilize and survive. 40% damage mitigation is a LOT of damage mitigation
Being perma slow is a major drawback, but I have escaped the creek of dookie many times by switching to melee while wearing my Fists of Steelbilly when a situation goes sour <3
One thing I loved that Halo pointed out was to play as medic. Playing medic will absolutely make you a better heavy. When you are looking for places to hide as medic, it will stick in your mind when you are playing heavy. Trying to keep your medic where they have some cover is a fantastic way to get on a monster KS. Halo's note on communication is key, too. The best medics know to stay out of blast range while working the vents when possible - if you tailgate the heavy as medic, you will find out the hard way that your 150 HP is WAY less than his 450 overheal; splash damage from pills and rockets will ruin your good time
One last thing I like to do when I know a medic and I will be camping a spot is to do some preventive maintenance and throw a sandvich down before the guano gets into the fan blades. This works well with medics you know will 1) notice it is on the ground; 2) not pick it up when they are at 97% health. The other risk you run with a premeditated sandvich throw is that someone else might pick it up in the chaos – even the other team. I find it is worth the risk though; knowing I can keep JAWBREAKER singing not deprive the medic of a snack if they need it is usually credit to team
If you toss it where you know the medic will be hiding it is in an area that you are defending anyway...
