I made this mod for personal use, but decided to publish it here in case someone else wanted these changes as well.
(And yes, I know my image editing skills are terrible!)

This is a very simple mod that changes the values of most base enchantments in the game (the ones used for enchanting).
The mod aims to make all enchantments useful and balance them out with enchantments you find on loot. I also wanted to make enchantments have round values on their strongest versions (100 skill + all enchanting perks without any enchantment potions).

The value of a base enchantment are the ones you see when viewing the enchantment BEFORE choosing it. They are multiplied by a skill factor (x1.25 at level 100) and perk bonuses (x2 from the Enchanter perk and another x1.25 from others).
In the end, it's strength will be Base x 2.5  x 1.25 (if you have perk) and I used this value to balance out.
For further information: http://en.uesp.net/wiki/Skyrim:Enchantments

Requirements: Skyrim Special Edition + Unofficial Skyrim Special Edition Patch.

ALL Changes:
Weapons:
Stamina/Magicka damage: 15 Attribute damage-> 20 Attribute damage
Made these generally stronger to encourage weapons made for sabotaging enemy mages or warriors. Max out at +50 damage.

Health/Stamina/Magicka Absorb: 8/10/10 Attribute Absorb -> 10/12/12 Attribute Absorb
Made these stronger so they can compete with the vanilla enchanted weapons.
They are weaker than the damage counterparts for obvious reasons. They max out at +25/30 Absorb.

Shock/Fire/Frost damage: 10 Elemental damage -> 12 Elemental damage
Made these slightly stronger to get a nice and round 30 elemental damage bonus (37 if you get the perk, which I personally wouldn't).

Huntsman's Prowess: 3 Animal damage -> 16 Animal damage
Make this enchantments much better. It's stronger than Shock/Fire/Frost damage, but since it's only for animals that's alright. Maxes out at +40 damage.

Silent Moons: +10 Light damage -> 12 Light damage
Slight stronger (just like Elemental damage). They can only be used at night (which can be easily manipulated) but don't have resistances to deal
with. Maxes out at 30 damage.

Paralyze: 2s -> 3s
Made stronger to compete with 6 sec paralyze Vanilla weapons. Max out at 7 sec.

Banish/Fear/Turn Undead: Level 10 -> Level 20 (no duration changes)
Significantly stronger so they can compete with vanilla enchanted weapons and are actually useful for once. Max out at level 50.

Soul Trap: 4s -> 8s
Significantly longer so it can compete with vanilla enchanted weapon. Max out at 20 sec.

Fiery Soul Trap: No change
The base length of 5 sec was unchanged to give incentive for using the non-fiery version. The fire damage part doesn't scale.

Chaos Damage: No Change
The base enchantment seems to scale differently, didn't touch it for now.

Apparel:
Fortify Magic Skill + Magicka Regeneration: +5 Fortify Magic Skill /+10% Magicka Regeneration -> +8 Fortify Magic Skill /+100% Magicka Regeneration
A set of completely useless enchantments, as they gave less cost reduction then the ones without Magicka Regeneration (for reference, the base value for those is 8). The +10% Magicka Regeneration bonus was too small and didn't scale with Enchanting skill/perks. Now, they give the same amount of spell cost reduction and also have a respectable Magicka Regeneration bonus, making them very attractive for any magic-based character. They can only be put on Robes/Body Armor, so they aren't too overpowered.

Fortify Alchemy/Magic Skill/Barter/Armor Skill/Smithing: No Change
These were plenty strong as is in my opinion. Max out at +25% improvement.

Fortify Archery/Block/One Handed/Two Handed/Lockpick/Pickpocket/Sneak: +13  -> +8
Made these significantly weaker so they get in line with other Skill enchantments and aren't as overpowered.

Fortify Health/Stamina/Magicka: +20 Attribute -> +24 Attribute
A small buff to these so that you can get up to +75 attribute bonus, which is slightly stronger than the +70 gear you can find.

Fortify Health/Stamina/Magicka Regeneration: +10/10/20 Attribute Regeneration Rate -> 16/16/32 Attribute Regeneration Rate
A big buff to make these compete with vanilla enchantments and more attractive for enchanting. They now reach +50/50/100% Regeneration Rate.

Resist Disease/Fire/Frost/Magic/Poison/Shock: +25/15/15/8/15/15% Resist -> +20/16/16/8/20/16% Resist
Re-scaled for round beautiful numbers. Magic resistance was untouched as it's already very powerful. They max out at +50% for Poison and Disease, +40% for Elemental (+50% if you pick the perks) and +20% for Magic.

Fortify Carry Weight: +15 Carry Weight - > +20 Carry Weight
Buffed this one by a bit to make it competitive with vanilla gear and to get a nice and round +50 Carry Weight bonus.

Fortify Unarmed: +5 Unarmed damage - > +10 Unarmed damage
Although it isn't very useful to most players, I felt that +12 unarmed damage (strongest you can get) was too low. Now it can get up to 25, which is
equivalent to most weapon enchantment bonus damage.

Waterbreath/Muffle: No Change
These don't really scale so I didn't touch them.

Ideas for future improvements:
- Find a way to scale the Magicka regeneration in Robe enchantments and Fire damage in Fiery Soul with level/perks.
- Change Chaos damage.