What's the noun for spindliness? Here's the word you're looking for.
spindle
(spinning) A rod used for spinning and then winding natural fibres (especially wool), usually consisting of a shaft and a circular whorl positioned at either the upper or lower end of the shaft when suspended vertically from the forming thread.
A rod which turns, or on which something turns.
A rotary axis of a machine tool or power tool.
Certain of the species of the genus Euonymus, originally used for making the spindles used for spinning wool.
An upright spike for holding paper documents by skewering.