TL;DR?
25 to 35 is generally where you want a stat to get the most out of it,
with a harder breakpoint at ~50

Methodology:
I created a new character and left him at lvl 1, ran around collected all the items I could from the areas before the 1st boss then used cheat engine to give this toon 9 million souls
From there I hand recorded the value changes in the levelup menu from 1 to ~120 for each stat without ever committing - these values were recorded using v1.01 of the game

The raw data is available here:
https://www.dropbox.com/s/wief4pqoebg772m/Hellpoint%20data.ods

Breakpoints:
5 = 99
11 = 145
19 = 200
31 = 270 <<< Optimal
51 = 363
71 = 435
110 = 537

Breakpoints:
13 = 73
30 = 100
50 = 120 <<< Optimal

Breakpoints:
10 = 75
25 = 115 <<< Optimal
50 = 155

Linear growth for as many points as I put into it.

ALWAYS put in at least 1 point, but from then on - only increase it by 3s; eg
2, 5, 8, 11, 14, 17, 20, etc - this takes advantage of the rounding error to gain 1 extra point


Mobility = based on what %age of your MAX load you are wearing
0-50% = no penalties
51-75% = ?
76-100% = can only run when sprinting; otherwise, you walk - which can be useful at times
101+% = can never run nor sprint

Weapon stats are harder, the whole point of an analysis like this is to see where the rounding errors give you a slight advantage... but there are a lot of weapons... and even for a single weapon you can change its scaling factor depending on what you slot into it... and that slot has upgrades of its own...

So I can give examples, but this section can't be used as a hard rule like the others can be.

Strength - Pipe Breakpoints (w/o anything slotted):
6 = 15 damage
17 = 18
35 = 21 <<< Optimal
54 = 23
80 = 25
118 = 27

Strength - Column Breakpoints (w/o anything slotted):
20 = 37 damage
33 = 41 <<< Optimal
41 = 43
51 = 45
69 = 48
84 = 50
113 = 53
124 = 54

Reflex - Shard Breakpoints (w/o anything slotted):
7 = 8 damage
15 = 9
25 = 10 <<< Optimal
39 = 11
60 = 12
89 = 13
130 = 14

If you are wondering where Cognition and Foresight are - the displayed numbers simply would not scale for me on weapons that claimed to scale with these stats so... idk!
Maybe it is just a display error /shrug

1st, ALL defenses follow the same leveling curve; it is only WHAT levels each one that changes:
Physical = Level (aka EVERYTHING contributes to the total)
Entropy = Energy
Induction = Load
Radiation = Strength
Energy = Reflex (yes, a 2nd "Energy" stat, that confused me too - it is should be called "Light")
Nihil = Foresight

Breakpoints:
2 = 1%
10 = 5%
22 = 9%
30 = 11% <<< Optimal
48 = 14%
57 = 15%
67 = 16%
79 = 17%
95 = 18%
115 = 19%

If you have any constructive critismism or helpful comments - I welcome such feedback.
Or if you have any questions I'll do my best to help out.
Otherwise thank you for taking a look at my guide. :)
And remember to rate, like, and favorite this guide if you found it helpful :D