heavy armor doesn't stop bullets, but should

heavy should be super-effective against (at least) pistols. See https://youtu.be/nlwlKEeJ0vU?t=303 for reference

I agree weight and movement speed cost is too high for only some slight protection against nades.

No, it shouldn't. Heavy armor straight-up stopping bullets would be gamebreaking. TTK is already too high compared to Insurgency. Being "super-effective" (which I assume to mean stopping 4+ shots) would make it a higher TTK than Call of Duty and other similar modern military shooters. At that point, it would be closer to TF2, Overwatch, Dirty Bomb, etc. than Insurgency.

even if heavy armor is effective against bullet it should still hurt af, imagine getting punch by 300m/s metal ball on your stomach

While I don't agree with what OP's saying exactly, I do think Heavy Armor should at least do something in-game, because right now it really doesn't do jack shit. Helps against battle rifles, some handguns, and some SMGs, but it makes literally no difference against any assault rifle, shotgun, or LMG.

I think the heavy armor does soak a few rounds, what i'd suggest is nerfing light armor and have no armor a 1 shot kill no matter the caliber (with exceptions to extremeties)