Poise Pasta

An easy way to think of how poise works in DaS2 is to imagine an invisible bar that increases over time, like poison or bleed or toxic buildup. The maximum value is your current poise, and when you get hit the bar goes up and you recover pretty quickly. A good way to observe this is with bosses, who will sometimes get staggered from an attack that was no different than your other attacks. This is due to this "bar" system.

However, there are some things to keep in mind:
Hyperarmor exists on some weapons, this means that no matter what it won't interrupt your attack DURING THOSE FRAMES.
After backstabbed or parried, your poise regains at roughly half the normal rate. If you've ever been staggered coming out of a wakeup attack, this is why.
When in this state, the meter must top off or bottom out in order to return to normal recharge rate.
Your recharge rate is not a percentage like you might think it would be, but a CONSTANT number. Someone with 50 poise recharges poise at the same rate as someone with 200 poise.
This trait of poise is the most important to keep in mind - sometimes even though the number says you have 120 poise, who knows, maybe you only have 30 poise. More poise gives you the effect of having slower recharge rate for a longer period of time after backstabs/parries, also.
Imagine it this way, two people get one apple a second. One person has a barrel that can hold five apples and the other has a barrel that can hold ten. Obviously, the man who has the larger barrel will take longer to fill.
Shield breaks don't have this same property as backstabs and parries, counter-intuitively. You don't have the regen penalty for some reason, even though you'd think that it would be the only one TO have the penalty.
When 2 handing a weapon, the poise damage it does is doubled. This includes the stone ring in its calculation, so if you're two handing with the stone ring you're getting another 60 poise damage. A katana has 20 poise damage, so it equals a total of 100 poise for a non-counter hit.
I'll bet you wonder why I said a non-counter hit. Well that's because poise damage is also modified by the counter multiplier, but this time it doesn't include the stone ring. The total poise damage of a chaos blade without latency but 2-handed with stone ring is 120 poise.
Another absurdity is that if the game desyncs while the weapon's hitbox is still inside your hitbox is that the poise damage is calculated again, because the game thinks it's a different hit entirely. This means that with a desync the chaos blade could wind up doing over 240 poise damage.
Back to hyperarmor for a second because this is also important - if they hit you when the hyperarmor frames are up, your hyper armor means fuck all. Ever since the nerf with great weapons hyper armor, this means that if they just delay their attack a little they can stagger you and interrupt your attack.
Something worth mentioning - after you're staggered the regen rate of your poise increases for until you top out. This is not a point in the favor for heavy armor like you think it is, because the regen rate is absurdly fast and might as well be instant. After this, you get a brief period of hyperarmor which is why you can roll out of attacks now. This didn't used to be the case, as anyone who was alive for the greatsword/tanirush meta can attest to.
When using strong attacks, your poise damage is increased by 1.5x
Powerstanced weapons are an interesting matter. Let's take powerstanced Chaos blades for an example.
Powerstanced weapons are treated as 2h weapons. This is fine for powerstance moves which only have one hitbox, but for moves like the Chaos Blade powerstance L1 which has 2 hitboxes, the poise damage is doubled for a total of 200 effective damage. This is 240 on a counterhit. I don't think I have to say anything about this.
You might be wondering from all this "if you have hyperarmor after stagger how come powerstanced fists can fuck me up and stunlock so hard no matter what I'm wearing?"
Well this is why. The two attacks mean that they can drain all of your poise even while your poise has the increased, nearly instant charge rate. Luckily their knockback causes you to move out of range enough to roll. An easy way to see that this is the truth, is to try sometime to chain-stagger a boss by 2handing your weapon and hitting them the instant they come out of their stagger animation.
So in a nutshell, even though they reduce the actual damage in the calculations for powerstance, the poise damage is increased effectively twofold. Enough to instantly stagger most people.