Arm weight should be used in conjunction with the pronator and supinator muscles (many call this rotation) with the addition of in/out motions to facilitate the different lengths of each finger. Grouping will aid in your query about the other fingers for grouping partakes in the weight distribution of the arm. In other words, when employing weight, up/down, in/out, forward shifting, pronation and supination and, GROUPING, this will all give the forearm a "shape" which will make all the subsequent notes just effortlessly fall out of your hands. I don't want to use this analogy but, your hand becomes like a domino chain. None of the fingers are playing in isolation, they are all playing together BUT, you flex the one your are playing just a smidge so it is slightly lower. With all these movements combined, it is is possible to play down while your are lifting up giving you the set up for the next execution of gravity. Even if you are executing a tremolo or trill using only the pronator and supinator, there is still in/out and up/down. Even if you are doing something repetitions, using all these movements simultaneously means you are not using the same muscle fiber twice in a row meaning . . . . . NO TENSION. Each fiber has an opportunity to relax before called upon a second later. Except your pronator and supinator. They are practically indefatigable.
In regard to scales, you were probably taught to abduct the thumb under the palm and this locks up the abductors of the other fingers creating tension and uneven playing. It can also lead to ulnar or radial deviation which also hinders even playing. It also grinds with the index tendon but teachers don't seem to know this. Never cross the thumb under. Use the arm to move the hand (like you are waxing a car) and place the thumb where it needs to be next.
By using arm weight, pronation and a forward shift, your thumb will play effortlessly. As far as playing fast scales, there are several other movements for the rest of the hand to facilitate that. Even if you have all the correct movements, the inclusion of an incorrect movement such as finger abduction, isolation, ulnar or radial deviation, can hinder progress. You must have all the correct motions and none of the incorrect ones.
No part of piano playing should be done in isolation. Consider casting a fishing pole. You don't cast from the wrist. You don't cast from the elbow. You don't cast from the shoulder. You cast from all three AND, in addition to that, they are aided by your legs, hips, abs and back. Likewise, piano playing isn't necessarily in the fingers, it is predominately in the arm. The arm places the finger, the finger doesn't drag the arm. Just as poking someones eye with your finger happens with the finger, it comes from the shoulder. Turning a doorknob doesn't happen in the wrist, it happens in the elbow (or should (pronator and supinator)).
We all know to pick up a piece of paper off the floor by bending the knees but, we are rarely taught how to be ergonomic with our arms.
You need to find a teacher who knows about the arm's anatomy, mechanical nature and physics. There has been three hundred years of poor teaching by people who don't know what they are doing and it just keeps getting passed down. It is a shame but I would estimate that over 90% of the teachers out there should not be teaching. This goes for gym teachers, too.
Find a good teacher who knows what they are doing who can re-train you. Call the Edna Golandsky school in NYC and ask if they have a teacher in your area.
If you complain to your teacher about tension, pain, fatigue, or that you can't play something, and they say "Practice more," "relax" or they assign a finger exercise (your fingers have no muscles), never go back to that teacher. You are wasting time and money. Not that they can't teach you other things but, they will cripple you from their ignorance of anatomy.