For me natural weight means weight of the arm resting on the strings through the hook formed by first finger and thumb of the bow hold. With nothing, no "crane muscles," on top of the arm holding back. To me this produces a nice earthy tone by bending the hair around the string and suppressing some of the upper partials, and sounds no more than about mf.
To use this weight smoothly and effectively from end to end of the bow without lifting I rotate the elbow up and out slightly which turns the bow hold in and throws weight forward onto the index finger. Only a few degrees, in order to align the elbow (hinge joint) movement with the bow direction. This works well for ON STRING playing.
For OFF STRING and SEMI-OFF playing I lower the elbow until bow hold fingers are parallel with the stick and I can "pat" the string with a shallow carried bounce. This works well near the balance point of the bow, that magic place that makes string crossing easy, and produces nice warm quaver speeds that I call "Haydn/Mozart" (try the opening of Eine Kleine Nachtsmusik).
SPICCATO could be as far out as the middle of the bow and require a different approach again because the string is more struck with a steeper "vee" shape by rotating the bow around the thumb. Generally bass players are allowed to produce spiccato closer to the balance point because our strings are so heavy.
So, my bow hold keeps changing according to the demands of the music. Three big variables come into play - bow speed, weight and contact point - also take into account which string you are playing on (the heavier the string the slower the bow)
The further you bow from the bridge the faster the bow must move to support and drive the vibrations. I prefer to bow closer, say near half way between fingerboard and bridge where the string is stiffer, and use a little more weight with a slightly slower bow. I listen for resonance, tone and projection while encouraging free movement of the strings even though the weight of my arm is bending the hair around them and controlling them.
Try this experiment. Wrap your fist around the frog. Crush the bow down on the D string and slowly draw a screeching BUT EVEN sounding down bow (like drawing your fingernails down the blackboard at school, remember!). Repeat this again and again, gradually reducing the weight and you will start to hear the note come out, still hopelessly crushed, from under the bow. Finally the full beautiful tone will emerge, the string will be moving freely and the bow hair will still be bent around the string!! Then go to the proper bow hold and copy. This is my model sound that I try to apply to all notes, all strings, as a starting point in sound production.
I do believe in using the natural weight of the arm for on-string playing. How I set my bow and bow arm to achieve this would take much more space to explain.