Passive bonuses. That's what. Some off the cuff thoughts:
Strength - Increases block/melee damage by x% (small increments), less encumbrance debuff, Increased stack sizes (Can you imagine the frothing rage?) reduced stamina use in melee
Perception - Faster zoom speed with scoped weapons, higher chance of a critical hit, chance to find additional loot in containers
Fortitude - x% damage resist, +x% (fractional) additional hp per level, debuff effects reduced by x%
Agility - x% less fall damage, jump x% higher/farther, x% chance to dodge an attack that would normally hit, reduced ADS time, faster reload speed
Intellect - x% less crafting time of things in the science category, x% better barter pricing, % chance to find additional scrap in loot, more harvest from mechanical/electronic blocks
You could go farther and have perks that would add bigger "chunks" to a specific thing like chance to find an additional item by 3% instead of .25% or whatever to further specialize, or have "synergy perks" that require 2 or more attributes to be at a certain level.