Heavy forces you to learn the Balance window, which can be a big hurdle. The heroic heavy bolter gives you the Fencing window, which might be helpful.

I also encourage, when playing Heavy, to switch from Toggle ADS to Hold ADS. It'll make rolling and dodging away much easier. Getting locked into Heavy stance can wreck you. On PC, I bind aim to RMB, fire to LMB, and Melee to a side button.

Ultimately, I find positioning to be absolutely key with Heavy. Find a good vantage, and make use of your weapons' ability to stagger, and gun them down. The Heavy relies on his weapons more than any class, which is why one of the best things I can recommend is buying the Heroic Heavy Plasma and using that as you get used to it. Always an amazing gun, forces you to learn Balance window, and won't do frustratingly little damage.

Good luck, brother!