I've tried both, weighted and unweighted options in some particular dialogues and came to a conclusion that in some dialogues the game just wants you to fail by design, when in other situations it lightens the grip and dice are cast randomly indeed. At least that's how it felt, for there was no difference between the two options for me.
Even if charisma (for example) will bring the requirement to a minimum 6, the dice will give you 1, 2, 5, until you spend that blasted point, which actually increases your chances greatly. Time and time again I kept drawing a short stick... Painful... I won't pretend to know how randomization works in this game but it doesn't feel random at all.
In a fight, with weighted die on, my warrior managed to miss 4 turns in a row, no hexes or debuffs were in play, just my freakin' luck.
Though, I have to admit, it was a memorable moment, normally each character doesn't exceed 3 misses in a row.