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A man creates robot arms to manipulate the world as he is disabled. The arms created larger and larger arms and smaller and smaller arms so they can perform gigantic and microscopic tasks? Any idea what story this is from?

Odds are that this is Robert A. Heinlein's "Waldo"

Waldo Farthingwaite-Jones was born a weakling, unable even to lift his head up to drink or to hold a spoon. Far from destroying him, this channeled his intellect, and his family's money, into the development of the device patented as "Waldo F. Jones' Synchronous Reduplicating Pantograph". Wearing a glove and harness, Waldo could control a much more powerful mechanical hand simply by moving his hand and fingers. This and other technologies he develops make him a rich man, rich enough to build a home in space.

In the story, these devices became popularly known as "waldoes". In reference to this story, the real-life remote manipulators that were later developed also came to be called waldoes, some even by NASA. Later, an American company, The Character Shop, which creates animatronic devices and objects (often for motion pictures), obtained the trademark to Waldo for "data-capture input devices".

....

A typical illustration of the tools in the story is Waldo's handling of his need to perform micro-dissection on the scale of cellular walls. He uses human-sized waldoes to make smaller waldos, then uses those to make even smaller waldoes, and continues the series until he has waldoes small enough to work at the cellular scale.

There are three main factors involved in Heinlein's description of the tools:

• They work like human hands: not with a single active lever or twenty different tools, but with components arranged and with actions like human hands. The operator puts his or her hands in "gloves" and the waldos repeat the movements of the hands.


• They work in conjunction with viewing equipment that lets the user see the waldos as if they have the size and action of his own hands. This, in conjunction with the first factor, means that waldos are a "no-training" tool: if you know how to use your hands, you can use waldos.


• They allow work to be done remotely, in the next room or many miles away, or in an environment that could kill a human or be contaminated by human presence. They can be a different size from normal human hands: either huge for building construction or tiny for micro-manipulation.

This sounds like Robert Heinlein's 'Waldo', a 1942 short story
about a character with some arm-strength problems (myasthenia
gravis is mentioned).