Some mobs with tools/weapons are not affected by the weakness effect.

Steps to Reproduce:

1. Summon a zombie. (/summon zombie)
2. Give him a sword. (/replaceitem entity @e[type=zombie] slot.weapon.mainhand 0 diamond_sword)
3. Give him weakness. (/effect @e[type=zombie] weakness 1000 255
4. Let him hit you.

Observed Results:

He damages you.

Expected Results:

He can’t damage you.

Notes:

You can use every tool/weapon you want. 
(Affected tools/weapons: 
Swords, tridents, axes, pickaxes, shovels, hoes)

I only tested this with zombies, husks, wither skeletons, skeletons (I gave him an axe) and drowned.