My guess would be that it has to do with rounding & the way the end value is calculated based on the scalars.
For your helmet at the end there, you may not see an increase at +5 since a low base value * 5ilvl of difference * scalar isn't enough to push it into the next tier (or it may have rounded up into that tier to begin with and didn't hit a value high enough to exceed the tier after +5), but +10 or +15 certainly should reflect a difference.
you can see here on a low-ilvl item how it doesn't always increase.
That is, the aspects are calculated similarly to [base value] * [item power + blacksmith upgrade] * [unknown scalar] * [equip slot scalar]
I say similarly because I can't quite get estimated values to match up with ingame values cleanly.
The rest is napkin math:
For example, with a codex'd pulverized aspect on 1h 803+25, the base value is 1.05. The same aspect on 2h 192+15 is 0.61, and on 192+20 is 0.65.
Normalizing to 1h, .305 at i207 and .325 at i212. So over 616 ilvls, a base diff of 0.725.
0.725 / .02 (the base inc) = 36.25, so assuming 828 is mid-tier, 36.25 tier jumps over 616 ilvls = 16.993 or every ~17 ilvls the base value is expected increase on average. But this is only based off 3 data points, is not reliable, and is just an approximation.
Given ilvl 192 and aspect tooltip dps of 63
if x = 1 (assuming no bsm scalar); base/2 * 192 = 63
192b = 126
b = 126/192 = 0.65625, which we know is untrue as that's > the base value at i207
so there must be hidden/base value scalar even at +0
base/2 * 192x = 63, if base = 0.61 (possibly less)
.61/2 * 192x = 63
.305 * 192x = 63
58.56x = 63
x = ~1.07582
0.61/2 * (192+15) * x * 2 = 140
.305 * 207 * 2 = 140
126.27x = 140
x = ~1.108735
0.65/2 * (192+20) * x * 2 = 154
.65 * 212 * x = 154
137.8x = 154
x = ~1.117562
x diff btw +15 and +20 ~0.88264%
192 (+15) -17 is still within an estimated tier, but is possibly 1 tier lower.
so if base = 0.305-0.02 = 0.285, x should be closer to 10%
0.285 * 192x = 63
54.72x = 63
x = ~1.151316
too high, so more likely to be within the same tier (0.305 base) with a lower scalar (~1.07582)
it's also possible that the base value increases in stepped amounts (e.g. +0.01, +0.02, +0.01, +0.02) at more frequent intervals or something.
Again, not enough data points.
But we can clearly see the ranges as "126-180", "140-200", and "154-220" at 2h values -> "63-90", "70-100", "77-110" 1h in increments of [7-10]. So in order for the blacksmith upgrade to actually upgrade the aspect, 0.61/2*[192+y]*x has to be closer to the new tier,
I think.
e.g. if we assume a 10% scalar for example's sake, 0.61/2 * 192+5 *1.1 = ~66.1, 63 < 66.1 < 70, and is closer/still within the 63-90 tier, so doesn't upgrade. But 0.61/2 * 192+10 *1.1 = ~67.8 which does upgrade, being closer to the next tier.
Although, it could also be a matter of exceeding that min threshold, with the game rounding up to the nearest integer.
If we increase the scalars slightly,
0.305 * 192+5 * 1.11 = ~66.7 -> 67
0.305 * 192+10 * 1.12 = 69.0032 -> 70, tier break
nothing conclusive to garner from all this just that
tl;dr, +5 ilvls upgrade isn't enough to break into a new tier, probably.
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