General:
At level 5, you gain 2 ninjutsu skill points and 2 samurai skill points, regardless of where you spend your points.
You gain another 2 samurai skill points for every additional 5 levels.
You gain 10 HP per level, and additional HP if you level Body or Stamina.
Body:
(I'm including the total health bonus, so subtract 10 from these values if you're comparing to other stats)
6: +40HP
7: +35HP
8: +35HP
9: +30HP
10: +30HP
11 onward: +25HP (Tested up to 75)
vs Poison and vs Paralysis gain +1 per 5 points starting at 6, capping out at +10 at 51 points.
Also grants 1 samurai skill point per two points.
Heart
6-15: about +2.1 Ki per point (either 2 or 3 per level, +21)
15-40: +1 ki per point
40+: +1 ki per two points (Tested up to 75)
Also grants 1 samurai skill point per two points.
Stamina
6: +1 max weight
7: +0.9 max weight
8: +0.9 max weight
9: +0.8 max weight
10: +0.8 max weight
11: +0.7 max weight
12: +0.7 max weight
13: +0.6 max weight
14: +0.6 max weight
15: +0.5 max weight
16: +0.6 max weight
17: +0.5 max weight
...from this point on it gets weird, it's rounded fractional amounts. Basically it very slowly tapers off, no softcaps.
74: +0.2 max weight
75: +0.1 max weight
HP: Slight softcap at 10. 11 onward: +15HP (Tested up to 75)
Also grants 1 samurai point per 2 points.
Strength
+0.1 Equip Weight Max and +5 Ki Pulse until 10
+0.05 Equip Weight Max and +3.5 Ki Pulse until 15
Equip Weight Max slowly tapers off again. It might be a logarithmic function, it looks like this.
Ki pulse also slowly tapers off. No softcap, but 40+ is +1 ki pulse per point. 50+ is 1 per 2 points.
Also grants 1 samurai point per 1 point.
Skill
Ki pulse is double the bonus per point of Strength, with identical scaling.
+2 Ninjutsu Power until 10, then +1 Ninjutsu Power per point
Also grants 1 samurai point per 1 point.
Dexterity
Ninjutsu Power: Slight softcap at 10, then very slow and gradual diminishing returns. (Basically the moral of the story of how Nioh stats work). 9 power per point at 11, scaling down to 3 power per point at 75.
Ninjutsu Capacity: Hardcap at 30 Dexterity (total of 30 capacity)
Ninja Skill Points: 2 skill points per point, no cap.
15 Dexterity is required to complete the mission "The Way of the Ninja: Veteran", which is a sort of softcap.
Magic
Almost identical to dexterity.
Magic Power: Slight softcap at 10, then very slow and gradual diminishing returns. 9 power per point at 11, scaling down to 3 power per point at 75.
Magic Capacity: Hardcap at 30 Magic (total of 30 capacity)
Magic Skill Points: 2 skill points per point, no cap.
15 Magic is required to complete the mission "The Way of the Onmyo: Veteran", which is a sort of softcap.
Spirit
Magic Power: Similar scaling to Magic, about 1/3rd of the strength.
Guardian Bond: Slight softcap at 10, slow diminishing returns. 50 per point up to 10 going down to 10 per point at 70+.
vs. Yokai Realm: 2.5 per point, no diminishing returns or cap.
25 Spirit will unlock every ability from every guardian spirit, which is a sort of hardcap.
TL

R;
Most stats have a minor softcap at 10.
Health (Body and Stamina) softcaps at 10, then stays linear.
Ki (Heart) softcaps at 15 and again at 40.
Equip weight max slowly tapers off with no softcap.
Ki pulse is weird and I don't even know what it actually does.
Anything that gives skill points stays linear forever with no cap.
Magic and ninja power slowly tapers off with no softcap.
Magic and ninja capacity both hardcap at 30.
Figuring out weapon scaling is going to take way more science.