In Elden Ring, Quality is equivalent to quality.The word Quality comes from Demon's Souls and it lowers the base of a weapon to improve both the str and dex scaling. So let's say a weapon scales in strength as E and Dexterity as D, making it a Quality weapon could change the scaling to D/C. So if you had 40str and 40dex, you'd get more attack power, even though the base attack of a quality weapon was lower b/c you're getting more from the improved scaling of the weapon.
In Elden Ring, i think it's Keen that is the equivalent to quality. Heavy is for just str and so on.
Keen is for dex.