Hi, i like the cannons, and i would like your advices to up the accuracy of the heavy to make it more efficient. What is the best combination, for you? Armor? skills? multi (mix?) class? weapon?, etc…
(for example, do you think it’s good to replace the helmet and legs with those of the sniper? and compensate the less armor in putting points in strength, to increase HPs?)
For my heavy with cannon I typically choose the accuracy perks (“heavy weapon proefficacy” and “cautions”), combine it with a tech helmet with accuracy from New Jericho and you are fine. If you want to boost your accuracy further, multi class with sniper and choose “master marksman”. You can also change the heavy legs to NJ assault legs for good armor with no penalties.
So a good overall combination ist NJ tech helmet, heavy body and assault legs. It is decent accurate and armored with decent speed. Go with 30 str. for high HP and carry weight for 3 different weapons (+ rocket launcher) and all situations.
This way i play it at the moment.
The heavy is basically a weapon platform. 
I used different solutions dependent of what I want to have.
Close combat - No acc boost at all, standard NJ heavy armor all around for Jetpack and protection. I mostly switch the Hel II to Deceptor for Rage Burst, sometimes mixing in a melee weapon if he has the proficiency perk for it (the brawler perk also increases normal melee attacks) or a shotgun and additionally the Goliath grenade launcher + a rocket launcher for mid to long range stuff for situations when I can’t go close. This type of heavy don’t need much accuracy for his gun when he goes close in, what in most cases I want to have, but of course he needs armor and strength as much as he can get. Thanks to the grenade and rocket launcher I have with this build a pretty versatile unit for many cases from close up to long range and generally I like it as it is without changing to much in favour for accuracy.
Mid range explosive specialist - Very often I end up with sniper armor parts on the head and legs and the Neural Torso bionic augmentation to mount rockets and this one also provides an accuracy boost. His main weapons are mostly the grenade and rocket launcher but also the Hel II for some direct fire, sometimes also the Deceptor, but I don’t want to go to much in trouble with such a build. I found this build pretty effective on mid to long ranges because the accuracy boost is very handy for the Hel II and also decreases the scattering of the launchers even on max range.
The unique all in one master of Heavies - using a jetpack torso and the unique helmet and legs from the living weapons pack, these are heavily armored and also provide a little accuracy boost instead of a penalty. This is mostly the setup for my first and often also main heavy throughout the whole game. Main weapons are again Deceptor, grenade and rocket launcher and what ever I can get from personal perks. I dual class him to Infiltrator to get access to Sneak Attack + Vanish and with this combination I can only call such a build pretty OP.
So with the exception of the one unique build I mostly not mix up heavy torso armor with other parts to boost accuracy, instead I use the mobility of the jet pack to bring him as close as I can. This is also very handy for, in my opinion, his best low level skill, War Cry.
Edit:
I forgot to mention that I mostly switch to the Detiny III laser mount when I have access to it. For this there is IMO no need for any accuracy boost.
Ryu and MadSkunky, thank you very much to have took time for answer and for your advices that i’m going to analyse! 
Not sure how no one said this but the anu stomper lega are great for the heavy
Plus 20 acc and 30 armor
Edit: typos
Oh, i didn’t know this, thank you too, The DayBreaker!
There are also 2 good builds with accuracy and speed in mind:
perceptor head + anvil-2 torso + agile legs
disruptor head + anvil-2 + agile legs
Both have +10 accuracy, +3 movement, immunity to goo, jetpack and mounted weapon. Perceptor gives better perception for nice heavy overwatches while disruptor gives neural disruption which now works as intended for sirens and scyllas.
Not much armor in the head and legs, though. However, these are not close-quarters builds and the most easy to hit part is the torso which is heavily armored. As MadSkunky said, when you get the Destiny III your heavies will be hitting from afar and these builds are good for that while also giving enough movement for your heavy to move around if needed AND shoot in the same turn.
If you dual class him with sniper then… you get even better accuracy from afar with master marksman, great and cheap overwatch (specially with perceptor head) from extreme focus, and cheaper AP shots with quick aim. Also, you can even carry a sniper rifle for when you’re just too far for a reliable canon shot, although I prefer to have an assortment of heavy weapons for any situation - canon, machine gun, grenade launcher and even flamethrower.
