Credit to u/Narabug on Reddit.
https://www.reddit.com/r/worldofpvp/comments/9hbnj4/tested_some_azerite_trait_scaling/

TLDR: Azerite trait dmg and healing scales inversely to your equipped iLVL. Traits with static numbers (not percentage based) will scale exponentially by lowering your equipped iLvL.

"PvP Scaling Magic" -
Damage - You become more balanced as you and your enemies iLvl are closer together. If your iLvl is significantly lower and your enemies is significantly higher, you will deal more and take less damage from them, and they will deal less and take more damage from you.

Healing - You will heal your teammates less if you lower your iLvl and they have a higher iLvl. However, they will be able to heal you significantly more in proportion to your total HP when your iLvl is low and the healers iLvl is high.

UPDATE:
Based on peoples testing it seems like the optimal gear setup would be -

Highest iLVL Azerite gear with triple stacked traits.
Low iLVL armor with the most gem sockets possible and most optimal secondary stats for your spec. Also, old world gear with special bonus effects on them.

The bonuses from lowering your iLvL seem to taper off once you get below 300 or above 370.

Some quotes from posters in this thread.

made a 300 ilvl triple gushing lacerations azerite trait set. (increased rip damage)

tested with a friend who was 358 ilvl and my rip did on average around 700 more damage per tick on his screen, along with all my other dots and abilities doing increased damage too.

Damage reduction for dropping ilv is legit tho
^this^

You can do more damage depending on your azerite trait stacking
You take less damage (amazing for rbg tanks btw)
It's more reliant on your azerite traits.
you also do less healing.

Tested healing with a friend too,
regrowth crit him 29k at 358 ilvl, 138k hp
regrowth crit him 29k at 298 ilvl, 98k hp
(heals aren't scaled when healing lower ilvl players)

So with this in mind:
The optimal 3s setup would be two dps with no trinkets equipped, optimized gear offstats around 300 ilvl for reduced damage taken. (don't forget azerite triple trait stack)
healer still stays max ilvl for increased heals.

lower ilvl with azerite trait stacking scales damage done/taken and azerite traits but not heals

Let the chaos ensue.