Why is the thermometer tube, through which mercury rises or falls, or alcohol is made thin?

The thermometer tube consists of two parts: a relatively large reservoir is connected to a small diameter tube (capillary). The reservoir is filled with liquid. The headspace is evacuated. When the massive tip is heated, the volume of the liquid increases and is pushed into a thin tube, opposite which there is a scale. The smaller the section of the tube, the greater its length will be taken by the same increment in the volume of the liquid.
Let v – volume increment, l – fluid column length increment, s – tube cross-sectional area:
l = v / s.
When the thermometer cools down, a free volume forms in the tip, where the liquid is drained from the capillary. By changing the cross-section of the tube, you can change the sensitivity of the thermometer.
In addition, with a sufficiently large diameter of the tube, the surface tension forces of the liquid may not be sufficient to form a clear interface. The liquid will gain freedom and the ability to flow from one part of the tube to another.