Cut down to just the parts I want to focus on here.

What make "a scout with a shotgun" a "weaker player" than you?

To get the kill, they need to have passed all the way through your optimal range, and they still have to land 3 shots on you at point-blank almost-melee range without letting you get a bead on them for the approximately 0.5s it takes to reduce their paper suit into a pile of scrap with something that used to be a body inside its swiss-cheesed remains. If they're too far, it can take 4 or 5 shots to finish a well-fitted Heavy with even a high-tier Shotgun.

If you let that happen, you're as bad as a tank driver complaining about AV when he's running without support. You screwed up, your enemy punished you for it. Heavies are the Scout's natural prey. You need someone to keep them off you, just like most front-line Assaults need someone to keep the Heavies from steamrolling through them. And just like all the AR guys need some friends with AV capabilities to keep the tanks from rolling through and wiping them out.

Part of your complaint is that your Heavy suit was dying fast to a low-RoF weapon designed specifically for the range bracket you ended up in with no effectiveness if you managed to kill them while they were moving into position.

But in response to this part, I disagree. IF they add damage mitigation, it should be a baseline advantage to Heavies to help balance out the fact that they get shafted at higher tiers, because that IS a legitimate complaint. Other suits get better by a larger margin than Heavies do as you skill up, particularly when you consider the price of Heavy suits. They could, like they do with vehicles, add damage reduction modules as well.

We call them shield extenders, a complex one will reduce the damage from an AR by a whole 2 bullets.

Actually, shield extenders win almost every single time, even with the broken damage mods. Disturbingly Board did the math.
All though I think we are supposed to get resistance modules if I remember right.

But then there's the fact that, as fixed-value bonuses, Shield Extenders aren't subject to stacking penalties. While not currently working as intended, Damage Mods SHOULD be limited in that regard.

And I think it would be interesting to have a Shield Resistance Amplifier that reduces damage while your shields are still up, or an Armour Hardener that reduces damage to your suit's armour.

And I think it would be a good idea if, as I said, Heavies got a "built-in" bonus to damage reduction, just like Logi suits get a built in hacking bonus and Scouts get a built-in advantage to scanning range. At their current capabilities, though, Low-tier Heavies are about where they should be, so it should be a bonus that they gain as you skill up. Give (for example) a 3% damage reduction bonus on Advanced suits, and a 5% bonus for Prototype. Or 5% and 10%, maybe. I don't know. I'd rather see them brought into line with the other suits than over-buffed though, so I'm leaning towards a smaller bonus instead of a larger one.

But I DON'T agree with giving the other suits a passive bonus of this kind when they're already otherwise well-balanced within each tier. They used to have HP increased (both Shield and Armour) as you upgraded to the new suits, and that made a well-fitted Proto Assault more of a Heavy than a Standard Heavy suit could ever be. They NEEDED to make the advantage boil down to how you fit the improved suits, rather than the baseline stats being better.

are you playing a lot of corp battles for 15 mil where that heavy proto is necessary, or are you whoring kills in ambush in that thing?

That's the game in a nutshell: the suit is merely the centerpiece of your fitting, and if you prioritize all your SP on getting the best suit right away, then you have accomplished little more than increasing the cost of your deaths. It's the combined accumulation of a variety of passive skills and high level gear that really makes you more powerful.