Well, my ideal solution to weapons/armor would be that there are no weapon/armor proficiency categories but that all weapons/armor have minimum Strength requirement and more strength you are missing, more penalties you have.
Also, for melee weapons(and thrown) you can use str or dex if you have required strength.
ranged is dex based as normal.
for weapons: if you do not have sufficient strength, you have disadvantage to attack and deal minimum damage. and cannot use dex for melee weapons.
for armor: for every str mod that you are missing, you have -1 to attack, -1 for spell DCs, -1 to str and dex checks and saves and -5ft speed penalty.