So the solution would be quadratic classes which would disempower ability scores.
Additional you you would need to increase the proficiency bonus and limit ability bonuses to max +3
Abilities would require a slight make-over
Strength - affects weight allowance, weapon usage and damage (including ranged) and str-based skill checks
Dexterity - affects to hit, initiative, armour class and dex-based skill checks
Constitution - affects recovery time, system shock and exhaustion checks
Intelligence - affects Int spell level limit, additional proficiencies, languages and int-based skill checks
Wisdom - affects Wis spell level limit, wis-based skill checks, limits no of background flaws
Charisma - affects Cha spell level limit, attunement, cha-based skill checks
Casters characters - spell DCs affected by level, every 3 levels = +1DC, specialists gain +1DC on their chosen school
Martial characters - damage affected by level and proficiencies/expertise/specialisation
Hit Points based on Level + Size
Races would also require a retool.
EDIT: I'm just gonna add this here before anyone else does