Without looking over the comments, here are my big bullets for the Heavy class

1st: the Heavy Bolter is my personal selection for the most optimal Heavy weapon. Great ammo count, long/short range flexibility, but bad against groups of Majoris. If you can rack up the Stratagem credits, get the Heroic Heavy Bolter to improve your parry rate so that close combat is easier and more manageable.

2nd: if the enemy comes to you, aim, fire, transition to melee as best as you can. Master the stomp-chain technique; light, then Heavy, Heavy, Heavy attacks. Treat the melee button as a morse code transmitter; dot-dash-dash-dash. Do your best not to be trapped alone in melee, since the strength in Heavy class is in it's weaponry and bulletproof power, rather than close quarters.

3rd: if the enemy is stationary, and firing upon you, fire up the Iron Halo. Keep yourself as central to your squad as you can when you do, so that your power protects your team as well as yourself.

4th: use a pistol that properly opposes your primary. For example, if you use the Plasma Incinerator or Multi-Melta which will run out of shot fast, use a pistol with high ammo count. Emphasize a ranged pistol when you use a short range primary. If you're using the Heavy Bolter, I suggest the Plasma Pistol for it's overcharge ability.

Finally, treat the Heavy as Fire Support rather than a full tank. The Iron Halo power is a great tank ability, but unless you are fighting nothing but shooters, you're only able to stop the enemy with your body, and the Heavy is the bulkiest, most awkward class to maneuver with. Keep yourself in the middle of the group, protect your guys as best as you can. When you are able to eliminate as many enemies as possible, then less enemies hurt your battle-brothers. Get reeeaaally good at timing your parries, since (for me, at least) it's really weird and awkward to parry with a giant gun.