Is it balanced?
Sure, it's balanced if you apply it to all sides of a combat equally. It's a very minor change. Even taking into account characters with multiple attacks each round, it's a couple of HP here or there - not worth worrying about.
Is it worthwhile?
No. You're adding complexity in the pursuit of verisimilitude. That's a fine idea, except that your method goes against the basic system design - D&D5E is not a margins-of-success system, it's a pass-or-fail system. There are other systems where the core mechanics include margin-of-success and have your glancing blows built in. That said, I don't think it adds enough verisimilitude to make the complexity worth while - you're adding an additional parameter check for a whole three damage.
D&D is not a reality simulator.
What you should be looking to do is describe your combats differently. Look at some real sword fighting if you can, or some Hollywood sword fighting if you can't. A sword fighter doesn't swing once every six seconds.
In D&D, one attack roll represents a series of swings, backpedals, feints, dodges, and the glancing blows you're looking for. It's all aggregated into a single roll to keep complexity down. Even "Extra Attack" isn't really extra attacks, the character isn't swinging significantly faster than they were before, but they're so good they can get in more blows that matter.
In the PHB (page 196) we have:
Hit points represent a combination of physical and mental durability, the will to live, and luck. Creatures with more hit points are more difficult to kill. Those with fewer hit points are more fragile.
In other words, it's possible to lose hit points without taking any penetrating injury, from a glancing blow. Take a character with a shield: sometimes, the "hit" that "gets through" is not actual wounds, they're an expenditure of energy and effort in getting the shield in the way or the pain and discomfort from the enemy wailing on the shield. In a similar vein, a "hit" on a lightly armored character could actually be a "miss" dramatically, but the character twists or over extends something in the effort to get out of the way. It may not even hurt right now (adrenaline and all that), but it'll hurt later.